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Yang, Xue. "Neumann problems for second order elliptic operators with singular coefficients." Thesis, University of Manchester, 2012. https://www.research.manchester.ac.uk/portal/en/theses/neumann-problems-for-second-order-elliptic-operators-with-singular-coefficients(2e65b780-df58-4429-89df-6d87777843c8).html.
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In this thesis, we prove the existence and uniqueness of the solution to a Neumann boundary problem for an elliptic differential operator with singular coefficients, and reveal the relationship between the solution to the partial differential equation (PDE in abbreviation) and the solution to a kind of backward stochastic differential equations (BSDE in abbreviation).This study is motivated by the research on the Dirichlet problem for an elliptic operator (\cite{Z}). But it turns out that different methods are needed to deal with the reflecting diffusion on a bounded domain. For example, the integral with respect to the boundary local time, which is a nondecreasing process associated with the reflecting diffusion, needs to be estimated. This leads us to a detailed study of the reflecting diffusion. As a result, two-sided estimates on the heat kernels are established. We introduce a new type of backward differential equations with infinity horizon and prove the existence and uniqueness of both L2 and L1 solutions of the BSDEs. In this thesis, we use the BSDE to solve the semilinear Neumann boundary problem. However, this research on the BSDEs has its independent interest. Under certain conditions on both the "singular" coefficient of the elliptic operator and the "semilinear coefficient" in the deterministic differential equation, we find an explicit probabilistic solution to the Neumann problem, which supplies a L2 solution of a BSDE with infinite horizon. We also show that, less restrictive conditions on the coefficients are needed if the solution to the Neumann boundary problem only provides a L1 solution to the BSDE.
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Kulkarni, Mandar S. "Multi-coefficient Dirichlet Neumann type elliptic inverse problems with application to reflection seismology." Birmingham, Ala. : University of Alabama at Birmingham, 2009. https://www.mhsl.uab.edu/dt/2010r/kulkarni.pdf.
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Thesis (Ph. D.)--University of Alabama at Birmingham, 2009.Title from PDF t.p. (viewed July 21, 2010). Additional advisors: Thomas Jannett, Tsun-Zee Mai, S. S. Ravindran, Günter Stolz, Gilbert Weinstein. Includes bibliographical references (p. 59-64).
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Karimianpour, Camelia. "The Stone-von Neumann Construction in Branching Rules and Minimal Degree Problems." Thesis, Université d'Ottawa / University of Ottawa, 2016. http://hdl.handle.net/10393/34240.
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In Part I, we investigate the principal series representations of the n-fold covering groups of the special linear group over a p-adic field. Such representations are constructed via the Stone-von Neumann theorem. We have three interrelated results. We first compute the K-types of these representations. We then give a complete set of reducibility points for the unramified principal series representations. Among these are the unitary unramified principal series representations, for which we further investigate the distribution of the K-types among its irreducible components.
In Part II, we demonstrate another application of the Stone-von Neumann theorem. Namely, we present a lower bound for the minimal degree of a faithful representation of an adjoint Chevalley group over a quotient ring of a non-Archimedean local field.
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Guo, Sheng. "On Neumann Problems for Fully Nonlinear Elliptic and Parabolic Equations on Manifolds." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1571696906482925.
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PERROTTA, Antea. "Differential Formulation coupled to the Dirichlet-to-Neumann operator for scattering problems." Doctoral thesis, Università degli studi di Cassino, 2020. http://hdl.handle.net/11580/75845.
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This Thesis proposes the use of the Dirichlet-to-Neumann (DtN) operator to improve the accuracy and the efficiency of the numerical solution of an electromagnetic scattering problem, described in terms of a differential formulation. From a general perspective, the DtN operator provides the “connection” (the mapping) between the Dirichlet and the Neumann data onto a proper closed surface. This allows truncation of the computational domain when treating a scattering problem in an unbounded media. Moreover, the DtN operator provides an exact boundary condition, in contrast to other methods such as Perfectly Matching Layer (PML) or Absorbing Boundary Conditions (ABC). In addition, when the surface where the DtN is introduced has a canonical shape, as in the present contribution, the DtN operator can be computed analytically. This thesis is focused on a 2D geometry under TM illumination. The numerical model combines a differential formulation with the DtN operator defined onto a canonical surface where it can be computed analytically. Test cases demonstrate the accuracy and the computational advantage of the proposed technique.
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Alcántara, Bode Julio, and J. Yngvason. "Algebraic quantum field theory and noncommutative moment problems I." Pontificia Universidad Católica del Perú, 2013. http://repositorio.pucp.edu.pe/index/handle/123456789/96072.
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Alsaedy, Ammar, and Nikolai Tarkhanov. "Normally solvable nonlinear boundary value problems." Universität Potsdam, 2013. http://opus.kobv.de/ubp/volltexte/2013/6507/.
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We study a boundary value problem for an overdetermined elliptic system of nonlinear first order differential equations with linear boundary operators.
Such a problem is solvable for a small set of data, and so we pass to its variational formulation which consists in minimising the discrepancy. The Euler-Lagrange equations for the variational problem are far-reaching analogues of the classical Laplace equation. Within the framework of Euler-Lagrange equations we specify an operator on the boundary whose zero set consists precisely of those boundary data for which the initial problem is solvable. The construction of such operator has much in common with that of the familiar Dirichlet to Neumann operator. In the case of linear problems we establish complete results.
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Orey, Maria de Serpa Salema Reis de. "Factorization of elliptic boundary value problems by invariant embedding and application to overdetermined problems." Doctoral thesis, Faculdade de Ciências e Tecnologia, 2011. http://hdl.handle.net/10362/8677.
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Dissertação para obtenção do Grau de Doutor em
MatemáticaThe purpose of this thesis is the factorization of elliptic boundary value problems defined in cylindrical domains, in a system of decoupled first order initial value problems. We begin with the Poisson equation with mixed boundary conditions, and use the method of invariant embedding: we embed our initial problem in a family of similar problems, defined in sub-domains of the initial domain, with a moving boundary, and an additional condition in the moving boundary. This factorization is inspired by the technique of invariant temporal embedding used in Control Theory when computing the optimal feedback, for, in fact, as we show, our initial problem may be defined as an optimal control problem. The factorization thus obtained may be regarded as a generalized block Gauss LU factorization. From this procedure emerges an operator that can be either the Dirichlet-to-Neumann or the Neumann-to-Dirichlet operator, depending on which boundary data is given on the moving boundary. In any case this operator verifies a Riccati equation that is studied directly by using an Yosida regularization. Then we extend the former results to more general strongly elliptic operators. We also obtain a QR type factorization of the initial problem, where Q is an orthogonal operator and R is an upper triangular operator. This is related to a least mean squares formulation of the boundary value problem. In addition, we obtain the factorization of overdetermined boundary value problems, when we consider an additional Neumann boundary condition: if this data is not compatible with the initial data, then the problem has no solution. In order to solve it, we introduce a perturbation in the original problem and minimize the norm of this perturbation, under the hypothesis of existence of solution. We deduce the normal equations for the overdetermined problem and, as before, we apply the method of invariant embedding to factorize the normal equations in a system of decoupled first order initial value problems.
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Boller, Stefan. "Spectral Theory of Modular Operators for von Neumann Algebras and Related Inverse Problems." Doctoral thesis, Universitätsbibliothek Leipzig, 2004. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-37397.
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In dieser Arbeit werden die Modularobjekte zu zyklischen und separierenden Vektoren für von-Neumann-Algebren untersucht. Besondere Beachtung erfahren dabei die Modularoperatoren und deren Spektraleigenschaften. Diese Eigenschaften werden genutzt, um Klassifikationen für Lösungen einiger inverser Probleme der Modulartheorie anzugeben. Im ersten Teil der Arbeit wird zunächst der Zusammenhang zwischen dem zyklischen und separierenden Vektor und seinen Modularobjekten mit Hilfe (verallgemeinerter) Spurvektoren für halbendliche und Typ $III_{\lambda}$ Algebren ($0<\lambda<1$) näher untersucht. Diese Untersuchungen erlauben es, das Spektrum der Modularoperatoren für Typ $I$ Algebren anzugeben. Dazu werden die Begriffe {\em zentraler Eigenwert} und zentrale Vielfachheit eingeführt. Weiterhin ergibt sich, dass die Modularoperatoren durch ihre Spektraleigenschaften eindeutig charakterisiert sind. Modularoperatoren für Typ $I_{n}$ Algebren sind genau die $n$-zerlegbaren Operatoren, die multiplikatives, zentrales Spektrum vom Typ $I_{n}$ besitzen. ähnliche Ergebnisse werden auch für Typ $II$ und $III_{\lambda}$ Algebren gewonnen unter der Vorausetzung, dass die zugehörigen Vektoren diagonalisierbar sind. Im zweiten Teil der Arbeit werden diese Ergebnisse exemplarisch auf ein inverses Problem der Modulartheorie angewendet. Dabei stellt sich heraus, dass die Begriffe zentraler Eigenwert und zentrale Vielfachheit Invarianten des inversen Problems sind und eine vollständige Klassifizierung seiner Lösungen unter obigen Voraussetzungen erlauben. Außerdem wird eine Klasse von Modularoperatoren untersucht, für die das inversese Problem nur ein oder zwei Lösungsklassen besitztIn this work modular objects of cyclic and separating vectors for von~Neumann~algebras are considered. In particular, the modular operators and their spectral properties are investigated. These properties are used to classify the solutions of some inverse problems in modular theory. In the first part of the work the correspondence between cyclic and separating vectors and their modular objects are considered for semifinite and type $III_{\lambda}$ algebras ($0<\lambda<1$) in more detail, where (generalized) trace vectors are used. These considerations allow to compute the spectrum of modular operators for type $I$ algebras. To this end, the notions of central eigenvalue and central multiplicity are introduced. Furthermore, it is stated that modular operators are uniquely determined by their spectral properties. Modular operators for type $I_{n}$ algebras are exactly the $n$-decomposable operators, which possess {\em multiplicative central spectrum of type $I_{n}$}. Similar results are derived for type $II$ and $III_{\lambda}$ algebras under the assumption that the corresponding vectors are diagonalizable. In the second part of this work these results are applied to an inverse problem of modular theory. It comes out, that the central eigenvalues and central multiplicities are invariants of this inverse problem and that they give a complete classification of its solutions. Moreover, a class of modular operators is investigated, whose inverse problem possesses only one or two classes of solutions
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Hänel, André [Verfasser]. "Singular Problems in Quantum and Elastic Waveguides via Dirichlet-to-Neumann Analysis / André Hänel." Aachen : Shaker, 2015. http://d-nb.info/1080762264/34.
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Ackermann, Nils. "Lokalisierung der niederenergetischen Lösungen eines singulär gestörten elliptischen Neumann-Problems mittels der Geometrie des Gebietsrandes." [S.l. : s.n.], 1999. http://deposit.ddb.de/cgi-bin/dokserv?idn=958029016.
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Verfasser], Afzal, and Günter [Akademischer Betreuer] [Neumann. "Re-plant problems in long-term no-tillage cropping systems : causal analysis and mitigation strategies / Afzal ; Betreuer: Günter Neumann." Hohenheim : Kommunikations-, Informations- und Medienzentrum der Universität Hohenheim, 2017. http://d-nb.info/1142977625/34.
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Alves, Michele de Oliveira. "Um problema de extensão relacionado a raiz quadrada do Laplaciano com condição de fronteira de Neumann." Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/45/45132/tde-19012011-231320/.
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Neste trabalho definimos o operador não local, raiz quadrada do Laplaciano com condição de fronteira de Neumann, através do método de extensão harmônica. O estudo foi feito com o auxílio das séries de Fourier em domínios limitados, como sendo o intervalo, o quadrado e a bola. Posteriormente, aplicamos nosso estudo, à problemas elípticos não lineares envolvendo o operador não local raiz quadrada do Laplaciano com condição de fronteira de Neumann.In this work we define the non-local operator, square root of the Laplacian with Neumann boundary condition, using the method of harmonic extension. The study was done with the aid of Fourier series in bounded domains, as the interval, the square and the ball. Subsequently, we apply our study, the nonlinear elliptic problems involving non-local operator square root of the Laplacian with Neumann boundary condition.
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Coco, Armando. "Finite-Difference Ghost-Cell Multigrid Methods for Elliptic problems with Mixed Boundary Conditions and Discontinuous Coefficients." Doctoral thesis, Università di Catania, 2012. http://hdl.handle.net/10761/1107.
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The work of this thesis is devoted to the development of an original and general numerical method for solving the elliptic equation in an arbitrary domain (described by a level-set function) with general boundary conditions (Dirichlet, Neumann, Robin, ...) using Cartesian grids. It can be then considered an immersed boundary method, and the scheme we use is based on a finite-difference ghost-cell technique. The entire problem is solved by an effective multigrid solver, whose components have been suitably constructed in order to be applied to the scheme.
The method is extended to the more challenging case of discontinuous coefficients, and the multigrid is suitable modified in order to attain the optimal convergence factor of the whole iteration procedure.
The development of the multigrid is an important feature of this thesis, since multigrid solvers for discontinuous coefficients maintaining the optimal convergence factor without depending on the jump in the coefficient and on the problem size is recently studied in literature.
The method is second order accurate in the solution and its gradient. A convergence proof for the first order scheme is provided, while second order is confirmed by several numerical tests.
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Cisternino, Marco. "A parallel second order Cartesian method for elliptic interface problems and its application to tumor growth model." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2012. http://tel.archives-ouvertes.fr/tel-00690743.
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Cette thèse porte sur une méthode cartésienne parallèle pour résoudre des problèmes elliptiques avec interfaces complexes et sur son application aux problèmes elliptiques en domaine irrégulier dans le cadre d'un modèle de croissance tumorale. La méthode est basée sur un schéma aux différences fi nies et sa précision est d'ordre deux sur tout le domaine. L'originalité de la méthode consiste en l'utilisation d'inconnues additionnelles situées sur l'interface et qui permettent d'exprimer les conditions de transmission à l'interface. La méthode est décrite et les détails sur la parallélisation, réalisée avec la bibliothèque PETSc, sont donnés. La méthode est validée et les résultats sont comparés avec ceux d'autres méthodes du même type disponibles dans la littérature. Une étude numérique de la méthode parallélisée est fournie. La méthode est appliquée aux problèmes elliptiques dans un domaine irrégulier apparaissant dans un modèle continue et tridimensionnel de croissance tumorale, le modèle à deux espèces du type Darcy . L'approche utilisée dans cette application est basée sur la pénalisation des conditions de transmission a l'interface, afin de imposer des conditions de Neumann homogènes sur le bord d'un domaine irrégulier. Les simulations du modèle sont fournies et montrent la capacité de la méthode à imposer une bonne approximation de conditions au bord considérées.
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Pfefferer, Johannes [Verfasser], Thomas [Akademischer Betreuer] Apel, and Arnd [Akademischer Betreuer] Rösch. "Numerical analysis for elliptic Neumann boundary control problems on polygonal domains / Johannes Pfefferer. Universität der Bundeswehr München, Fakultät für Bauingenieurwesen und Umweltwissenschaften. Gutachter: Thomas Apel ; Arnd Rösch. Betreuer: Thomas Apel." Neubiberg : Universitätsbibliothek der Universität der Bundeswehr München, 2014. http://d-nb.info/1054706824/34.
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Cekić, Mihajlo. "The Calderón problem for connections." Thesis, University of Cambridge, 2017. https://www.repository.cam.ac.uk/handle/1810/267829.
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This thesis is concerned with the inverse problem of determining a unitary connection $A$ on a Hermitian vector bundle $E$ of rank $m$ over a compact Riemannian manifold $(M, g)$ from the Dirichlet-to-Neumann (DN) map $\Lambda_A$ of the associated connection Laplacian $d_A^*d_A$. The connection is to be determined up to a unitary gauge equivalence equal to the identity at the boundary. In our first approach to the problem, we restrict our attention to conformally transversally anisotropic (cylindrical) manifolds $M \Subset \mathbb{R}\times M_0$. Our strategy can be described as follows: we construct the special Complex Geometric Optics solutions oscillating in the vertical direction, that concentrate near geodesics and use their density in an integral identity to reduce the problem to a suitable $X$-ray transform on $M_0$. The construction is based on our proof of existence of Gaussian Beams on $M_0$, which are a family of smooth approximate solutions to $d_A^*d_Au = 0$ depending on a parameter $\tau \in \mathbb{R}$, bounded in $L^2$ norm and concentrating in measure along geodesics when $\tau \to \infty$, whereas the small remainder (that makes the solution exact) can be shown to exist by using suitable Carleman estimates. In the case $m = 1$, we prove the recovery of the connection given the injectivity of the $X$-ray transform on $0$ and $1$-forms on $M_0$. For $m > 1$ and $M_0$ simple we reduce the problem to a certain two dimensional $\textit{new non-abelian ray transform}$. In our second approach, we assume that the connection $A$ is a $\textit{Yang-Mills connection}$ and no additional assumption on $M$. We construct a global gauge for $A$ (possibly singular at some points) that ties well with the DN map and in which the Yang-Mills equations become elliptic. By using the unique continuation property for elliptic systems and the fact that the singular set is suitably small, we are able to propagate the gauges globally. For the case $m = 1$ we are able to reconstruct the connection, whereas for $m > 1$ we are forced to make the technical assumption that $(M, g)$ is analytic in order to prove the recovery. Finally, in both approaches we are using the vital fact that is proved in this work: $\Lambda_A$ is a pseudodifferential operator of order $1$ acting on sections of $E|_{\partial M}$, whose full symbol determines the full Taylor expansion of $A$ at the boundary.
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Herbig, Anne-Katrin. "A sufficient condition for subellipticity of the d-bar-Neumann problem." Connect to this title online, 2004. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1090531326.
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Thesis (Ph. D.)--Ohio State University, 2004.Title from first page of PDF file. Document formatted into pages; contains vi, 55 p. : ill. Advisor: McNeal, J.D., Dept. of Mathematics. Includes bibliographical references (p. 54-55).
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Winkler, Max [Verfasser], Thomas [Akademischer Betreuer] Apel, Olaf [Akademischer Betreuer] Steinbach, and Roland [Akademischer Betreuer] Herzog. "Finite Element Error Analysis for Neumann Boundary Control Problems on Polygonal and Polyhedral Domains / Max Winkler. Universität der Bundeswehr München, Fakultät für Bauingenieurwesen und Umweltwissenschaften. Betreuer: Thomas Apel. Gutachter: Thomas Apel ; Olaf Steinbach ; Roland Herzog." Neubiberg : Universitätsbibliothek der Universität der Bundeswehr München, 2015. http://d-nb.info/1077773129/34.
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QUESNE, CAROLE. "Probleme d'ecran avec donnees de neumann singulieres." Nantes, 1996. http://www.theses.fr/1995NANT2091.
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S'etant une surface a bord, on s'interesse aux solutions d'une equation de poisson-helmholtz dans le complementaire de s, et verifiant des conditions de neumann sur chaque face de l'ecran s et une condition de radiation a l'infini. On etudie le cas ou le second membre f de l'equation de poisson-helmholtz est dans un espace a poids a l'infini et ou les donnees de neumann peuvent etre singulieres (masse de dirac par exemple). On donne un resultat d'existence et d'unicite pour les solutions u qui sont d'energie finie pres du bord de l'ecran. L'unicite est obtenue de facon classique par la condition de rellich. L'existence est montree par une methode de perturbation du probleme libre dans le cas des conditions de neumann homogenes, puis par relevement dans le cas non homogene. Un resultat de regularite de u est etabli, dans le cas d'une surface plane polygonale a angle droit ou complementaire d'un angle droit, en utilisant une formule de representation de u basee sur les techniques de wiener-hopf. On donne ensuite une formule de representation integrale generale de la solution u a l'aide de differents potentiels ; ce qui permet de ramener la resolution du probleme exterieur a la resolution d'une equation integrale hypersinguliere sur s. L'approximation numerique de u est faite par l'intermediaire de sa representation integrale, l'approximation de la solution de l'equation integrale etant faite par une methode d'elements finis d'ordre 1, nuls sur le bord de s, et avec un maillage uniforme. Des resultats numeriques sont donnes dans le cas d'un ecran plan carre et de donnees de neumann nulle sur une face de l'ecran et egale a une masse de dirac sur l'autre. Les tests numeriques ont permis de confirmer les estimations d'erreurs theorique
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Alsaedy, Ammar, and Nikolai Tarkhanov. "Spectral projection for the dbar-Neumann problem." Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2012/5861/.
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Baydoun, Ibrahim. "Transport laplacien, problème inverse et opérateurs de Dirichlet-Neumann." Thesis, Aix-Marseille 2, 2011. http://www.theses.fr/2011AIX22094.
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Le travail de ma thèse est basé sur ces 4 points :i) Transport laplacien d'une cellule absorbante :Soit un certain espèce (cellule) de concentration C(x), qui diffuse dans un milieu homogène et isotrope à partir d'une lointaine source localisée sur la frontière fermée $partial Omega_{0}$ vers une interface compact semi-perméable $partial Omega$ (membrane de la "cellule") à laquelle elle disparaisse àun taux d'absorption donné : W>=0. La concentration C (transport laplacien avec un coefficient de diffusion D) satisfaite le problème (P1) (voir la thèse). On s'intéresse à résoudre le problème (P1) en dimension dim = 2; 3 et à calculer les courants local et total à travers les frontières des $partial Omega$ et $partial Omega_{0}$ qui seront utiles pour résoudre le problèmeinverse de localisation. Pour faciliter les calculs et les rendre explicites, on prend $partial Omega$ et $partial Omega_{0}$ avec des formes géométriquement régulières, précisément des boules, en distinguant les deux cas : $Omega$ et $Omega_{0}$ sont concentriques ou non-concentriques. Pour le cas non-concentriques , on utilise la technique de transformation conforme et le développement orthogonal en série de Fourier pour résoudre le problème (P1) en cas bidimensionnel. Tandis que en cas tridimensionnel, on résout le problème (P1) en utilisant le développement orthogonal suivant les fonctions sphériques harmoniques.ii) Problème inverse de localisationOn s'intéresse dans cette partie à résoudre le problème inverse de localisation associé au problème (P1) où les domaines $Omega$ et $Omega_{0}$ sont considérés avec des formes géométriques régulières (précisément des boules) . Ce problème consiste à trouver les conditions de Dirichlet-Neumann sur $partial Omega_{0}$ (courant local, courant total) suffisantes pour déterminer la position de la cellule $partial$ (par rapport à $Omega_{0}$), dont ces conditions sont disponibles par une suite des mesures expérimentales.iii) Problème invesre géomètrique :Dans cette partie on traite un autre type de problème inverse qui consiste à trouver la forme géométrique de la cellule en sachant les conditions de Dirichlet-Neumann au bord extérieur(partial Omega_{0}) qui sont mésurables par une suite d'expérience. Ce type du problème, on l'appelle le problème inverse géométrique. On résout ce problème en utilisant des techniques concernant les fonctions harmoniques et les transformations conformes.iv) Opérateur de Dirichlet-NeumannOn étudie l'opérateur de Dirichlet-Neumann relatif au problème (P1) dans les dimension deux et trois en distinguant les deux cas concentriques et non-concentriques. Ensuite, on montre que cet opérateur de Dirichlet-Neumann engendre certain semi-groupe qu'on l'appelle semi-groupe de Lax. Enfin, on construit ce semi-groupe de Lax associé à cet opérateur en cas tridimensionnel concentriques afin de vérifier que ce semi-groupe admet les mêmes propriétés que celui dans le cas généralThe outline of my thesisi) Let some "species" of concentration C(p), x 2 Rd, diuse stationary in the isotropic bulk from a (distant) source localised on the closed boundary $partial Omega_{0}$ towards a semipermeable compact interface $partial Omega$ of the cell $Omega in Omega_{0}$ where they disappear at a given rate $W >= 0$. Then the steady field of concentrations C satisfy the problem $(P1)$. (see the Thesis). We interest to solve (P1) in Twodimensional and Tridimensional cases and to calculate the local and total flux in order to solving the localisation inverse problem. In order to make easy the calculations, we take $Omega$ and $Omega_{0}$ with a regularly geometricals forms by distinguishing the two cases : Concentrics and non-concentrics case. For the non-cncentrics case, we use the conformal mapping technique for resolving the problem (P1) in the twodimensional case. whereas in the tridimensional case, we use the development according to the spherical harmonics functions.ii) Localisation inverse problemThe aim of the localisation inverse problem is to find the necessary Dirichlet-to-Neumann conditions in order to determine the position of thecell $Omega$, where these conditions are measurable.iii) Geometrical inverse problemOur main results concerns a formal solution of the geometrical inverse problem for the form of absorbing domains. We restrict this study to two dimensions and we study it by the conformal mapping technique and harmonic functions.iv) Dirichlet-to-Neumann operatorWe study the Dirichlet-to-Neumann operatot relative to problem (P1) in the twodimensional and tridimensionnal cases by distinguishing the two cases : Concentrics and non-concentrics case. We prove that the Dirichlet-to-Neumann operator generates some semi-group, we call it the Lax semi-group. Finally we construct this semi group and verify that this demi-group satisfies the generals properties of a operator
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Neves, Sérgio Leandro Nascimento 1984. "Sobre o número de soluções de um problema de Neumann com perturbação singular." [s.n.], 2012. http://repositorio.unicamp.br/jspui/handle/REPOSIP/305907.
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Orientadores: Marcelo da Silva Montenegro, Massimo GrossiTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
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Resumo: Neste trabalho, consideramos uma classe de problemas de Neumann com perturbação singular e fazemos um estudo do número de soluções do tipo "single peak" que se concentram em um mesmo ponto. Estudamos casos de concentração no interior e na fronteira do domínio. Obtemos um resultado de multiplicidade exata que relaciona o número de tais soluções com o número de zeros estáveis de um campo vetorial associado
Abstract: In this work, we consider a class of Neumann problems with singular perturbation and we study the number of single peak solutions which concentrate at the same point. We study concentration in the interior and at the boundary of the domain. We obtain an exact multiplicity result which relates the number of such solutions with the number of stable zeros of an associated vector field.
Doutorado
Matematica
Doutor em Matemática
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Godoi, Juliano Damião Bittencourt de. "Problemas de autovalores de Steklov-Neumann e aplicações." Universidade Federal de São Carlos, 2012. https://repositorio.ufscar.br/handle/ufscar/5827.
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Previous issue date: 2012-03-26Universidade Federal de Sao Carlos
In this work we will obtain four main results of existence of weak solution, three of them to elliptic partial di_erential systems with nonlinear boundary conditions and the other to elliptic partial di_erential equations with nonlinear boundary conditions associated with operator p-laplacian. These results will be obtained when there is a kind of interaction among the reaction nonlinearities and the Neumann spectra and an interaction among the boundary nonlinearities and the Steklov spectra, associated with the systems or equations. The tool that we will use is fundamentally based on minimax methods in critical point theory.
Obteremos no presente trabalho quatro principais resultados de existência de solução fraca, três deles para sistemas de equações diferenciais parciais elípticas com condições de fronteira não lineares e o outro para equações diferenciais com condições de fronteira não lineares associadas ao operador p-laplaciano. Estes resultados serão obtidos quando houver uma certa interação entre as não linearidades de reação e o espectro de Neumann, e uma interação entre as não linearidades de fronteira e o espectro de Steklov, associados aos sistemas ou equações. A técnica que utilizaremos está, fundamentalmente, baseada em métodos de minimax da teoria do ponto crítico.
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Сирєєва, В. А. "Розв'язок задачі Неймана для однозв'язної області." Thesis, Сумський державний університет, 2013. http://essuir.sumdu.edu.ua/handle/123456789/40946.
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Задачею Неймана називають задачу про знаходження гармонічної
функції в заданій області, якщо відома її поведінка на нескінченності
та значення нормальної похідної на границі. До задач Неймана
зводяться задачі фізики, механіки суцільного середовища та ін.
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Zanger, Daniel Zvi. "Regularity and boundary variations for the Neumann problem." Thesis, Massachusetts Institute of Technology, 1997. http://hdl.handle.net/1721.1/43460.
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Sahutoglu, Sonmez. "Compactness of the dbar-Neumann problem and Stein neighborhood bases." Texas A&M University, 2003. http://hdl.handle.net/1969.1/3879.
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This dissertation consists of two parts. In the first part we show that for 1 k 1, a complex manifold M of dimension at least k in the boundary of a smooth
bounded pseudoconvex domain
in Cn is an obstruction to compactness of the @-
Neumann operator on (p, q)-forms for 0 p k n, provided that at some point
of M, the Levi form of b
has the maximal possible rank n − 1 − dim(M) (i.e. the
boundary is strictly pseudoconvex in the directions transverse to M). In particular,
an analytic disc is an obstruction to compactness of the @-Neumann operator on
(p, 1)-forms, provided that at some point of the disc, the Levi form has only one
vanishing eigenvalue (i.e. the eigenvalue zero has multiplicity one). We also show
that a boundary point where the Levi form has only one vanishing eigenvalue can
be picked up by the plurisubharmonic hull of a set only via an analytic disc in the
boundary.
In the second part we obtain a weaker and quantified version of McNealÂs Property
( eP) which still implies the existence of a Stein neighborhood basis. Then we give
some applications on domains in C2 with a defining function that is plurisubharmonic
on the boundary.
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Raynor, Sarah Groff 1977. "Regularity of Neumann solutions to an elliptic free boundary problem." Thesis, Massachusetts Institute of Technology, 2003. http://hdl.handle.net/1721.1/29353.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2003.Includes bibliographical references (p. 57-58).
We examine the regularity properties of solutions to an elliptic free boundary problem, near a Neumann fixed boundary. Consider a nonnegative function u which minimizes the functional ... on a bounded, convex domain ... This function u is harmonic in its positive phase and satisfies ... along the free boundary ... , in a weak sense. We prove various basic properties of such a minimizer near the portion of the boundary ... on which ... weakly. These results include up-to-the boundary gradient estimates on harmonic functions with Neumann boundary conditions on convex domains. The main result is that the minimizer u is Lipschitz continuous. The proof in dimension 2 is by means of conformal mapping as well as a simplified monotonicity formula. In higher dimensions, the proof is via a maximum principle estimate for ...
by Sarah Groff Raynor.
Ph.D.
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Pinton, Stefano. "Regularity of the dbar-Neumann problem and the Green operator." Doctoral thesis, Università degli studi di Padova, 2012. http://hdl.handle.net/11577/3426289.
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This thesis deals with the regularity of the dibar-Neumann problem and the tangential Cauchy-Riemann system. Chapter 1 deals with compactness estimates. We prove that they hold when "(CR P-property)" is satisfied. The approach consists of a tangential basic estimate in the formulation given by Khanh in his thesis which refines former work by Nicoara.
Chapter 2 discusses regularity of the dibar-Neumann problem. The first approach to regularity in geometric terms has been done by Boas Straube through the method of the "good vector field" T or "good defining function" r. On the one hand, this condition yields regularity; on the other this condition is fulfilled, if there exists a plurisubharmonic defining function r.
The vector field condition has been weekened by Straube to a multiplier condition. We substitute this condition with a quantified one.
Chapter 3 deals with Hypoellipticity for vector fields and sums of squares with loss of derivatives. Our contribute deals with exponential type vector fields instead of finite type vector fields.Questa tesi tratta la regolarità del problema dibar-Neumann e del sistema di Cauchy-Riemann tangenziale. Nel capitolo 1 si discute delle stime di compattezza. Si prova qui che esse sussistono in presenza della"(CR P-property)". Il nostro approccio si basa su una stima di base stabilita da T.V. Khanh che migliora risultati precedenti di A. Nicoara. Il Capitolo 2 tratta la regolarità del problema dibar-Neumann in assenza di stime di compattezza. Il primo approccio consiste nella condizione di ``buon campo vettore T" o ``buona funzione definitoria r. Da un lato questa condizione dà regolarità; dall'altro, essa è soddisfatta quando c'è una funzione definitoria plurisubarmonica r. La condizione di campo vettore è stata sostituita da una più debole condizione di tipo "moltiplicatore". Noi riprendiamo questa condizione e ne diamo una versione "quantificata". Il capitolo 3 tratta l'ipoellitticità con perdita di derivate sia per campi vettoriali sia per somme di quadrati. Il nostro contributo consiste nel trattare campi vettoriali modificati da campi di tipo esponenziale anzichè, classicamente, di tipo finito.
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Zaveri, Sona. "The second eigenfunction of the Neumann Laplacian on thin regions /." Thesis, Connect to this title online; UW restricted, 2006. http://hdl.handle.net/1773/5748.
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Strauss, Albrecht. "Integralformeln und a priori-Abschätzungen für das [delta bar]-Neumann-Problem." Bonn : [s.n.], 1988. http://catalog.hathitrust.org/api/volumes/oclc/18440543.html.
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Bouhsiss, Fouzia. "Quelques résultats d'unicité pour des problèmes elliptiques et paraboliques." Besançon, 2001. http://www.theses.fr/2001BESA2048.
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Wanderley, Gabriela Albuquerque. "Capillary Problem and Mean Curvature Flow of Killing Graphs." Universidade Federal da Paraíba, 2013. http://tede.biblioteca.ufpb.br:8080/handle/tede/7418.
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Previous issue date: 2013-05-13Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
We study two types of Neumann problem related to Capillary problem and to the evolution of graphs under mean curvature flow in Riemannian manifolds endowed with a Killing vector field. In particular, we prove the existence of Killing graphs with prescribed mean curvature and prescribed boundary conditions.
Estudamos dois tipos de problemas relacionados com a Neumann problema capilar e à evolução dos gráficos sob fluxo de curvatura média em variedades Riemannianas dotados com um campo de vetores Killing. Em particular, provamos a existência de Matar gráficos prescrito com curvatura média e condições de contorno prescritas.
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Almeida, Samuel Oliveira de. "Soluções para problemas elípticos envolvendo o expoente crítico de Sobolev." Universidade Federal de Juiz de Fora, 2013. https://repositorio.ufjf.br/jspui/handle/ufjf/1468.
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CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Neste trabalho estudamos a existência de soluções para problemas elípticos envolvendo o expoente crítico de Sobolev. Primeiramente, investigamos a existência de soluções para um problema superlinear do tipo Ambrosetti-Prodi com ressonância em 1, onde 1 é o primeiro autovalor de (−Δ,1 0 (Ω)). Além disso, estudamos resultados de multiplicidade para uma classe de equações elípticas críticas relacionadas com o problema de Brézis-Nirenberg, com condição de contorno de Neumann sobre a bola.
In this work we study the existence of solutions for elliptic problems involving critical Sobolev exponent. Firstly we investigate the existence of solutions for an Ambrosetti-Prodi type superlinear problem with resonance at 1 , where 1 is the first eigenvalue of (−Δ,1 0 (Ω)). Besides, we study multiplicity results for a class of critical elliptic equations related to the Brézis-Nirenberg problem with Neumann boundary condition on a ball.
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Kim, Mijoung. "The d-bar-Neumann operator and the Kobayashi metric." Texas A&M University, 2003. http://hdl.handle.net/1969/94.
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Tran, Vu Khanh. "A general method of weights in the d-bar-Neumann problem." Doctoral thesis, Università degli studi di Padova, 2010. http://hdl.handle.net/11577/3426529.
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This thesis works in partial differential equations and several complex variables that concentrates on a general estimate for $\bar\partial$-Neumann problem on domain which is $q$-pseudoconvex or $q$-pseudoconcave at the boundary point. Generalization of the Property ($P$) in [C84], we define the Property $(f\T-\M\T-P)^k$ at the boundary point. The Property $(f\T-\M\T-P)^k$ is a sufficient condition to get following estimate
{(f\T-\M)^k} \qquad \no{f(\Lambda)\mathcal M u}^2\le c(\no{\bar\partial u}^2+\no{\bar\partial^*u}^2+\no{u}^2)+C_\M\no{u}^2_{-1}
for any $u\in C^\infty_c(U\cap \bar{\Omega})^k\cap \T{Dom}(\dib^*)$. We want to point our attention that by the choice of $f$ and $\M$, $(f\T-\M)^k$ will be subelliptic estimate, superlogarithmic estimate, compactness estimate, subelliptic multiplier estimate...
Moreover, the thesis contains some applications of $(f\T-\M)^k$ and constructions of the Property $(f\T-\M\T-P)^k$ on some class of domains.Questa tesi tratta di Equazioni alle Derivate Parziali in Più Variabili Complesse e ha come obiettivo principale quello di stabilire una stima generale per il problema $\bar\partial$-Neumann su un dominio che è $q$-pseudoconvesso o $q$-pseudoconcavo in corrispondenza di un punto di bordo $zo$. Generalizzando la Proprietà $(P)$ di [C84], si introduce la Proprietà $(f\T-\M\T-P)^k$ in $z_o$. Essa dà luogo alla stima {(f\T-\M)^k} \qquad \no{f(\Lambda)\mathcal M u}^2\le c(\no{\bar\partial u}^2+\no{\bar\partial^*u}^2+\no{u}^2)+C_\M\no{u}^2_{-1} per ogni $u\in C^\infty_c(U\cap \bar{\Omega})^k\cap \T{Dom}(\dib^*)$ ove $U$ è un intorno di $z_o$. E' il caso di osservare che per opportune scelte di $f$ e di $\M$, la stima $(f\T-\M\T-P)^k$ coincide con le principali stime della letteratura quali quelle subellittiche, superlogaritmiche, di compattezza e infine quelle di moltiplicatore subellittico. La tesi ha anche l'obiettivo di esibire delle classi rilevanti di domini che godono della Proprietà $(f\T-\M\T-P)^k$ e di discutere letteratura recente sul problema $\bar\partial$-Neumann nel quadro di questa proprietà.
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Schreffler, Morgan F. "Approximation of Solutions to the Mixed Dirichlet-Neumann Boundary Value Problem on Lipschitz Domains." UKnowledge, 2017. http://uknowledge.uky.edu/math_etds/47.
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We show that solutions to the mixed problem on a Lipschitz domain Ω can be approximated in the Sobolev space H1(Ω) by solutions to a family of related mixed Dirichlet-Robin boundary value problems which converge in H1(Ω), and we give a rate of convergence. Further, we propose a method of solving the related problem using layer potentials.
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Hladky, Robert K. "Boundary regularity of the Neumann problem for the Kohn Laplacian on the Heisenberg group /." Thesis, Connect to this title online; UW restricted, 2004. http://hdl.handle.net/1773/5811.
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Houot, Jean Gabriel Tucsnak Marius. "Analyse mathématique des mouvements des rigides dans un fluide parfait." S. l. : S. n, 2008. http://www.scd.uhp-nancy.fr/docnum/SCD_T_2008_0146_HOUOT.pdf.
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LIMA, Natan de Assis. "Análise funcional não-linear aplicada ao estudo de problemas elípticos não-locais." Universidade Federal de Campina Grande, 2010. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/1225.
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CNPq
Neste trabalho usaremos algumas técnicas da Análise Funcional Não-Linear para estudar a existência de solução para os chamados Problemas Elípticos Não-Locais, entre os quais destacamos aqueles que incluem o operador de Kirchhoff [...]. * Para visualizar o resumo recomendamos do download do arquivo uma vez que o mesmo utiliza formulas ou equações matemáticas que não puderam ser transcritas neste espaço.
In this work we will use same techniques of Nonlinear Analysis Functional to study the existence of solutions for the some Nonlocal Elliptic Problems, among then those which include Kirchhoff operator [...]. * To preview the summary we recommend downloading the file since it uses mathematical formulas or equations that could not be transcribed in this space.
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Grando, Thiago. "Existência de soluções para uma classe de problemas com condição de Neumann." reponame:Repositório Institucional da UFABC, 2011.
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Román, Parra Carlos Patricio. "Large conformal metrics with prescribed sign-changing Gauss curvature and a critical Neumann problem." Tesis, Universidad de Chile, 2014. http://www.repositorio.uchile.cl/handle/2250/116845.
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Ingeniero Civil MatemáticoEn esta memoria se estudian dos problemas semilineales elípticos clásicos en la literatura: el problema de la curvatura Gaussiana prescrita en dimensión 2, y el problema de Lin-Ni-Takagi con exponente crítico en dimensión 3. En ambos se encuentran soluciones con reviente cuando el valor de un parámetro involucrado se aproxima a cierto valor crítico. En el primer capítulo se estudia el siguiente problema: Dada una función escalar $\kappa(x)$, suficientemente regular, definida en una variedad Riemanniana compacta $(M,g)$ de dimensión 2, se desea saber si $\kappa$ puede corresponder a la curvatura Gaussiana de $M$ para una métrica $g_1$, que es adicionalmente conforme a la métrica inicial $g$, es decir, $g_1=e^ug$ para alguna función escalar $u$ en $M$. Sea $f$ una función regular en $M$ tal que \equ{f\geq 0,\quad f\not\equiv 0, \quad \min_M f=0.} Sean $p_1,\ldots,p_n$ una colección de puntos cualesquiera en los que $f(p_i)=0$ y $D^2f(p_i)$ es no singular. Se demuestra que para todo $\la>0$ suficientemente pequeño, existe una familia de metricas conformes de tipo burbuja $g_\la=e^{u_\la}g$ tal que su curvatura Gaussiana está dada por la función que cambia de signo $K_{g_\la}=-f+\la^2$. Más aún, la familia $u_\la$ satisface \equ{u_\la(p_j)=-4\log \la -2 \log \left(\frac{1}{\sqrt2}\log \frac{1}{\la}\right)+O(1), \quad \la^2e^{u_\la}\rightharpoonup 8\pi\sum_{i=1}^n\delta_{p_i},} donde $\delta_p$ corresponde a la masa de Dirac en el punto $p$. En el segundo capítulo se considera el problema \equ{-\Delta u+\la u-u^5=0,\quad u>0 \quad \mbox{in }\Omega,\quad \ddn{u}=0\quad \mbox{on }\partial\Omega,} donde $\Omega\subset \R^3$ es un dominio acotado con frontera regular $\partial\Omega$, $\la>0$ and $\nu$ denota la normal unitaria exterior a $\partial\Omega$. Se demuestra que cuando $\la$ se apoxima por arriba a cierto valor explícitamente caracterizado en términos de funciones de Green, una familia de soluciones con reviente en un cierto punto interior del dominio existe.
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Malavazi, Mazílio Coronel 1983. "Problemas elípticos do tipo côncavo-convexo com crescimento crítico e condição de Neumann." [s.n.], 2013. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307128.
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Orientador: Francisco Odair Vieira de PaivaTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
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Abstract: The abstract is available with the full electronic document
Doutorado
Matematica
Doutor em Matemática
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Varchon, Nicolas. "Perturbation de domaine dans les E. D. P." Besançon, 2001. http://www.theses.fr/2001BESA2040.
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Le thème principal de ce travail est la stabilité des solutions d'équations aux dérivées partielles elliptiques ou paraboliques lorsque le paramètre de perturbation est le domaine sur lequel est définie l'équation. Nous souhaitons être en mesure de traîter des situations où les ouverts sont irréguliers, avec des coupures ou des bords de mesure positive. Dans une première partie, nous étudions la stabilité des solutions variationnelles d'une équation ellip- tique du second ordre avec des conditions de bord de type Neumann homogène. Le résultat principal est obtenu sur les familles d'ouverts du plan dont le nombre de composante con- nexes du complémentaire est uniformément borné et munie de la topologie de Hausdorff complémentaire. Sur ces familles, la stabilité des solutions est équivalente à la stabilité de la mesure de Lebesgue des ouverts dans les régions du plan où le terme d'ordre zéro apparaît dans l'équation. En particulier, sans ce terme, les solutions sont stables. Ce dernier point permet de prouver que parmi toutes les coupures joignñt plusieurs points fixes dans une membrane plane, il en existe une qui la laisse la plus résistante possible. La deuxième par- tie est consacrée à la stabilité du flux de solutions de l'équation de la chaleur parabolique semi-linéaire avec des conditions de bord de type Dirichlet homogène. On considère des per- turbations telles que les solutions du problème elliptique associé soient stables. On s'intéresse alors à la stabilité des variétés centrales définies au voisinage des points stationnaires non forcément hyperboliques. Il apparaît que sur les domaines perturbés, le flux de solutions possèdent des variétés invariantes locales qui sont des perturbations continues des variétés centrales.
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Pillay, Samara. "The narrow escape problem : a matched asymptotic expansion approach." Thesis, University of British Columbia, 2008. http://hdl.handle.net/2429/1428.
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We consider the motion of a Brownian particle trapped in an arbitrary bounded two or three-dimensional domain, whose boundary is reflecting except for a small absorbing window through which the particle can escape. We use the method of matched asymptotic expansions to calculate the mean first passage time, defined as the time taken for the Brownian particle to escape from the domain through the absorbing window. This is known as the narrow escape problem. Since the mean escape time diverges as the window shrinks, the calculation is a singular perturbation problem. We extend our results to include N absorbing windows of varying length in two dimensions and varying radius in three dimensions. We present findings in two dimensions for the unit disk, unit square and ellipse and in three dimensions for the unit sphere. The narrow escape problem has various applications in many fields including finance, biology, and statistical mechanics.
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Benson, A. "A new approach to the boundary integral method for the three dimensional Neumann problem." Thesis, University of Salford, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.356179.
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Silva, Ilma Aparecida Marques. "Existencia e comportamento assintotico de soluções para uma classe de problemas de Dirichlet e uma classe de problemas de Neumann." [s.n.], 2003. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306979.
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Orientador: Djairo Guedes de FigueiredoTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Doutorado
Doutor em Matemática
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Isaev, Mikhail. "Stability and instability in inverse problems." Palaiseau, Ecole polytechnique, 2013. https://pastel.hal.science/docs/00/91/22/98/PDF/these.pdf.
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Dans cette thèse nous nous intéressons aux questions de stabilité et d'instabilité dans certains problèmes inverses classiques pour l'équation de Schrödinger et l'équation acoustique en dimension d>=2. Les problèmes considérés sont le problème inverse de Gel'fand de valeurs au bord et les problèmes inverses de diffusion en champ proche et en champ lointain. Les résultats de stabilité et d'instabilité présentés dans cette thèse se complètent mutuellement et contribuent à une meilleure compréhension de la nature des problèmes précités. En particulier, nous démontrons des nouvelles estimations de stabilité globale qui dépendent explicitement de la régularité du coefficient et de l'énergie. En outre, nous considérons le problème inverse de valeurs au bord pour l'équation de Schrödinger à l'énergie fixée avec des mesures frontières représentées comme l'opérateur frontière d'impédance (ou l'opérateur Robin-Robin). Nous démontrons des estimations de stabilité globale pour détermination du potentiel à partir de mesures frontières dans cette représentation d'impédance. De plus, des techniques similaires donnent aussi une procédure de reconstruction globale pour ce problèmeIn this thesis we focus on stability and instability issues in some classical inverse problems for the Schrödinger equation and the acoustic equation in dimension d>=2. The problems considered are the Gel'fand inverse boundary value problem, the nearfield and the far-field inverse scattering problems. Stability and instability results presented in the thesis complement each other and contribute to a better understanding of the nature of the aforementioned problems. In particular, we prove new global stability estimates which explicitly depend on coefficient regularity and energy. In addition, we consider the inverse boundary value problem for the Schrödinger equation at fixed energy with boundary measurements represented as the impedance boundary map (or Robin-to-Robin map). We prove global stability estimates for determining potential from boundary measurements in this impedance representation. Moreover, similar techniques also give a global reconstruction procedure for this problem
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Neumann, Fanny [Verfasser], and Klaus [Akademischer Betreuer] Püschel. "Sexueller Missbrauch von Kindern in Hamburg - ein Vergleich der Fälle aus den Jahren 2005 und 2009 / Fanny Neumann. Betreuer: Klaus Püschel." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2013. http://d-nb.info/1031280286/34.
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Silva, CÃcero Fagner Alves da. "ExistÃncia e unicidade para os problemas de Dirichlet e Neumann sobre um domÃnio com fronteira suave." Universidade Federal do CearÃ, 2010. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=5286.
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CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel SuperiorSeja Ω um domÃnio fixado em Rn com fronteira S de classe C2 e denote Ω′ = Rn Ω. Ambos Ω e Ω′ nÃo necessariamente conexos. Nessas condiÃÃes, pretendemos resolver os problemas de Dirichlet e Neumann. No intuito da resoluÃÃo dos problemas citados, faremos um estudo daTeoria de Fredholm (operadores compactos), bem como da transformada de Kelvin, harmonicidade no infinito e dos potenciais de camada.
Let Ω be a fixed domain in Rn with boundary S of class C2 and denote Ω′ = Rn Ω. Both Ω and Ω′ not necessarily connected. Under these conditions, we intend to solve the problems of Dirichlet and Neumann. In order to overcome the mentioned the problems, we will study the Fredholm theory (compact operators), the Kelvin transformed, harmonicity in the infinite and potential of the layer.