Дисертації з теми "Liouville theorems"
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Fazly, Mostafa. "m-Liouville theorems and regularity results for elliptic PDEs." Thesis, University of British Columbia, 2012. http://hdl.handle.net/2429/43751.
Повний текст джерелаD'Ambrosio, Lorenzo. "Hardy Inequalities and Liouville Type Theorems Associated to Degenerate Operators." Doctoral thesis, SISSA, 2002. http://hdl.handle.net/20.500.11767/4170.
Повний текст джерелаMastrolia, P. "GRADIENT ESTIMATES AND LIOUVILLE THEOREMS FOR DIFFUSION-TYPE OPERATORS ON COMPLETE RIEMANNIAN MANIFOLDS." Doctoral thesis, Università degli Studi di Milano, 2011. http://hdl.handle.net/2434/153097.
Повний текст джерелаCunha, Antonio Wilson Rodrigues da. "Sobre hipersuperfÃcies mÃnimas, aplicaÃÃes do princÃpio do mÃximo fraco e de teoremas tipo-Liouville." Universidade Federal do CearÃ, 2015. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=15135.
Повний текст джерелаConselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico
In this work we approach four research lines, where we began with the study of isometrically immersed hypersurfaces in a horoball. Next we studied Liouville type theorems in a complete Riemannian manifold for general operators. After we studied hypersurfaces f-minimal closed on a manifold with density, and nally we studied properly embedded minimal hypersurfaces with free boundary in a n-dimensional compact Riemannian manifold. Continuing, we obtain under a more general class operator than '-Laplacian, a Liouville type theorem for a complete Riemannian manifold, so that, prove a classication theorem for Killing graph of a foliation. Firstly, we are going to assume a weak maximum principle and that immersion is contained in a horoball, i.e., the set of bounded above Bussemann functions . We obtain an estimate for the highest quotient of r-curvatures. Moreover, under certain conditions on sectional curvature and assuming that the immersion is contained in a horoball, we forced the validity of the weak maximum principle and obtain the same estimates. Next, we establish a Choi-Wang type estimate for the rst eigenvalue of the weighter Laplacian on spaces with density in responding partially to Yau's conjecture for the rst eigenvalue weighter Laplacian for spaces with density, and moreover, we obtain an inequality Poincare type. With the estimates obtained, we establish an estimate of volume for a closed surface immersed in a space with density. Still following the study of spaces with density, we obtain a type Hientze-Karcher inequality for a compact manifold with nonempty boundary , so that, we obtain that if holds the equality than the manifold is isometric to a Euclidian ball. As consequence, we obtain under same conditions that if the f-mean curvature satisfy a bounded below than the manifold is isometric to a Euclidian ball. Finally, we obtain an estimate for the nonzero rst Steklov eigenvalue, where we are giving a answer partial to a conjecture by Fraser and Li. Moreover, as a consequence we establish an estimate for the total length of the boundary of the properly embedded minimal surfaces with free boundary in terms of its topology, thus, we proved the same when the surface is embedded in the Euclidean ball 3-dimensional.
Neste trabalho, abordamos quatro linhas de estudo, onde iniciamos com o estudo de hipersuperfcies isometricamente imersas sobre uma horobola. Em seguida estudamos Teoremas tipo Liouville para uma variedade Riemanniana completa em operadores mais gerais que o Laplaciano. Alem disso, estudamos hipersuperfcies f-mÃnimas fechadas em uma variedade com densidade e, por fim, estudamos hipersuperfÃcies mÃnimas com bordo livre, propriamente imersas em uma variedade Riemanniana compacta n-dimensional. Primeiramente, assumindo um princpio do maximo fraco e que a imersÃo està contida em uma horobola, i.e., um conjunto em que a funcÃo de Busemann à limitada superiormente, obtemos uma estimativa para o supremo do quociente das r-Ãsimas curvaturas. AlÃm disso, sob certas condiÃÃes sobre as curvaturas seccionais e assumindo que a imersÃo està contida em uma horobola, forÃamos a validade do princÃpio do mÃximo fraco e obtemos as mesmas estimativas. Prosseguindo, obtemos, para um operador mais geral que o '-Laplaciano, um teorema tipo-Liouville para uma variedade Riemanniana completa. Como aplicaÃÃo provamos um teorema de classificaÃÃo para grÃficos de Killing de uma folheaÃÃo. Em seguida, estabelecemos uma estimativa tipo Choi e Wang para o primeiro autovalor do f-Laplaciano em espaÃos com densidade, no sentido de responder parcialmente à conjectura de Yau para o primeiro autovalor do Laplaciano; alÃm disso, obtemos uma desigualdade tipo Poincarà para esse operador. Com a estimativa obtida, pudemos estabelecer uma estimativa de volume para uma superfÃcie fechada mergulhada em um espaÃo com densidade. Ainda seguindo o estudo de espaÃos com densidade, obtemos uma desigualdade tipo Heintze-Karcher para uma variedade compacta com bordo e verificamos que, se vale a igualdade, entÃo a variedade à isomÃtrica a uma bola Euclidiana. Como consequÃncia, obtemos que, nas mesmas condiÃÃes, e se a f-curvatura mÃdia satisfizer uma certa limitaÃÃo inferior, entÃo a variedade ainda à isometrica a uma bola Euclidiana. Finalmente, obtemos uma estimativa para o primeiro autovalor de Steklov, dando uma resposta parcial a uma conjectura devida a Fraser e Li. AlÃm disso, como consequÃncia, estabelecemos uma estimativa para o comprimento do bordo de uma superfÃcie mÃnima, compacta e propriamente megulhada com bordo livre em termos de sua topologia; assim, provamos o mesmo resultado quando a superfÃcie està mergulhada em uma bola Euclidiana 3-dimensional.
Afonso, Rafaela Ferreira. "Um estudo do comportamento dos zeros dos Polinômios de Gegenbauer." Universidade Federal de Uberlândia, 2016. https://repositorio.ufu.br/handle/123456789/16825.
Повний текст джерелаIn this dissertation, we study the Sturm Liouvile's theorems for the zeros of the solutions of linear differential equations of second order. These classical theorems are applied to analysis of the monotonicity of functions involving the zeros of classical orthogonal polynomials. in particular, Gegenbauer polynomials.
Neste trabalho estudamos os Teoremas de Sturm Liouville para zeros de soluções de equações diferenciais lineares de segunda ordem. Estes teoremas clássicos são aplicados para análise do crescimento e decrescimento de certas funções que envolvem os zeros de Polinômios Ortogonais Clássicos, como os Polinômios de Gegenbauer.
Mestre em Matemática
Tupia, Martín Dionisio Arteaga. "A função de três pontos nas teorias de Liouville e N = 1 super Liouville." Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-24092015-135051/.
Повний текст джерелаIn this dissertation we present some basic features about Liouville and N=1 Super Liouville Theory, and focus in the computation of their three point functions. Additionally, we include an introduction to Conformal Field Theories (CFT) and Supersymmetry, which are the basic tools of the present research.
Bär, Christian. "Some properties of solutions to weakly hypoelliptic equations." Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2012/6006/.
Повний текст джерелаNeves, Rui Gomes Mendona. "Conformal field theories on random surfaces and the non-critical string." Thesis, Durham University, 1997. http://etheses.dur.ac.uk/4750/.
Повний текст джерелаLima, Jalman Alves de. "Teoremas Tipo Liouville e Desigualdades Tipo Harnack para Equações Elípticas Semilineares via Método Moving Spheres." Universidade Federal da Paraíba, 2011. http://tede.biblioteca.ufpb.br:8080/handle/tede/7400.
Повний текст джерелаCoordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In this work, we will do some applications of the Moving Spheres method, a variant of the method of Moving Planes, in order to obtain some Liouville-type theorems and some Harnack-type inequalities in Rn, as well as in the Euclidian half space Rn +. Our study focuses on, mostly, in the article written by Yan Yan Li and Lei Zhan [32], as well as some references of the same article. We concentrate in studying some properties of positive solutions of some semilinear elliptic partial differential equations with critical exponent and giving different proofs, improvements, and extensions of some previously established Liouville-type theorems and Harnack-type inequalities.
Neste trabalho, faremos algumas aplicações do método Moving Spheres, uma variante do método Moving Planes, na obtenção de alguns teoremas tipo Liouville e de algumas desigualdades tipo Harnack em Rn, bem como no semi-espaço euclidiano Rn +. Nosso estudo se concentra, marjoritariamente, no artigo do Yan Yan Li e Lei Zhang [32], bem como algumas referências do mesmo. Nos concentramos em estudar propriedades de soluções positivas de algumas equações diferenciais parciais elípticas semilineares com expoente crítico e dar provas diversificadas, refinamentos e extensões de alguns Teoremas tipo Liouville e desigualdades tipo Harnack já estabelecidos.
COLOMBO, GIULIO. "GLOBAL GRADIENT BOUNDS FOR SOLUTIONS OF PRESCRIBED MEAN CURVATURE EQUATIONS ON RIEMANNIAN MANIFOLDS." Doctoral thesis, Università degli Studi di Milano, 2021. http://hdl.handle.net/2434/813095.
Повний текст джерелаJackson, Henry Richard. "Exploring random geometry with the Gaussian free field." Thesis, University of Cambridge, 2016. https://www.repository.cam.ac.uk/handle/1810/263640.
Повний текст джерелаPolavieja, Gonzalo Garcia de. "Geometric phase and angle for noncyclic adiabatic change, revivals and measures of quantal instability." Thesis, University of Oxford, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.325986.
Повний текст джерелаDella, Sala Giuseppe. "Geometric properties of non-compact CR manifolds." Doctoral thesis, Scuola Normale Superiore, 2007. http://hdl.handle.net/11384/85684.
Повний текст джерелаCarvalho, Silas Luiz de. "Espectro e dimensão Hausdorff de operadores bloco-Jacobi com perturbações esparsas distribuídas aleatoriamente." Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-21122010-145625/.
Повний текст джерелаIn this work we attempt to caracterize the spectrum of a class of limited block--Jacobi operators defined in $l^2(\\Lambda,\\mathbb{C}^L)$ ($\\Lambda: \\mathbb{Z}_+\\times\\{0,1,\\ldots,L-1\\}$ represents a strip of width $L\\ge 2$ on the semi--plane $\\mathbb{Z}_+^2$) subject to a sparse perturbation (which means that the distance between the ``barries\'\' grow geometrically with their distance to the origin) randomly distributed. Such operators are defined as Kronecker sums of unidimensional Jacobi matrices $J$, each one acting in different directions of the space. We prove, by means of a block--diagonalization of the operator, that %the study of its most relevant spectral properties depend on %is related to the caracterization of the ``mixture measure\'\' $\\frac{1}{L}\\sum_{j=0}^{L-1}\\mu_j$, $\\mu_j$ the spectral measure of the Jacobi matrix $J^j=J+2\\cos(2\\pi j/L)I$. For this, we must characterize at first each one of the measures $\\mu_j$, exploiting and improving some well known techniques developed in the study of unidimensional sparse operators. We prove, for instance, that the sequence of Prüfer angles (variables which parametrize the solutions of the eigenvalue equation) are uniform distributed on the interval $[0,\\pi)$, a result which gives us condition to determine the average asymptotic behavior of the solutions of the eigenvalue equation. Such result, in association with the techniques developed by Marchetti \\textit{et. al.} in \\cite{MarWre} and with an adaptation of Last--Simon \\cite{LS} criteria for sparse operator, permit us to prove the existence of a sharp transition between singular continuous and pure point spectra. Following on, we use the results from Jitomirskaya--Last of \\cite{JitLast} and obtain the exact Hausdorff dimension of the measure $\\mu_j$, given by $\\alpha_j=1+\\frac{4(1-p^2)^2}{p^2(4-(\\lambda-2\\cos(2\\pi j/L))^2)}$ ($\\lambda\\in[- 2,2]$), recovering an analogous result due to Zlato\\v s in \\cite{Zla}. At last, we adapt these results to the mixture measure of the block--Jacobi matrix, obtaining $\\alpha=\\min_{j\\in\\mathcal{I}(\\lambda)}\\alpha_j$, $\\mathcal{I}(\\lambda):\\{m \\in\\{0,1,\\ldots,L-1\\}:\\lambda\\in[-2+2\\cos(2\\pi j/L),2+2\\cos(2\\pi j/L)]\\}$, as its exact Hausdorff dimension. We study as well identical models with sub and super geometric sparsities conditions, obtaining a pure point spectrum (with null Hausdorff dimension) in the first case, and a purely singular continuous spectrum (such that its Hausdorff dimension is 1) in the second. Finally, we prove the existence of a transition between pure point and singular continuous spectra in a model with sub--geometric sparsity whose Hausdorff dimension related to the spectral measure is null.
Mtiri, Foued. "Études des solutions de quelques équations aux dérivées partielles non linéaires via l'indice de Morse." Thesis, Université de Lorraine, 2016. http://www.theses.fr/2016LORR0150/document.
Повний текст джерелаThe main concern of this thesis deals with the study of solutions of several elliptic partial differential equations via the Morse index, including the stable solutions, i.e. when the Morse index is zero. The thesis has two independent parts. In the first part, under suplinear and subcritical assumptions on f, we establish firstly some explicit estimation for the L1 norms of solutions to -Δu = f(u) avec u = 0 on the boundary, via its Morse index. We propose an approach more transparent and easier than the work of Yang [1998], which allow us to treat some nonlinearities very close to the critical growth. These results motivated us to consider the polyharmonic equations (-Δ)ku = f(x; u) with especially k = 2 and 3. With the hypothesis on f similar to Yang [1998] and appropriate boundary conditions, we obtain for the _rst time some explicit estimations of solution via its Morse index, for the polyharmonic equations.In the second part, we consider a Lane-Emden system -Δu = ρ(x)vp; -Δv = ρ(x)u_; u; v > 0; in RN; with 1 < p< θ and a radial positive weight ρ. We prove the non-existence of stable solution in small dimension case. Our results improve the previous works Cowan & Fazly [2012]; Fazly [2012]; Hu [2015], especially we prove some general Liouville type results for stable solutions in small dimension which hold true for any 1 < ρ min(4 3 ; θ)
Garrione, Maurizio. "Existence and multiplicity of solutions to boundary value problems associated with nonlinear first order planar systems." Doctoral thesis, SISSA, 2012. http://hdl.handle.net/20.500.11767/4930.
Повний текст джерелаWang, Chao. "Analyse de quelques problèmes elliptiques et paraboliques semi-linéaires." Phd thesis, Université de Cergy Pontoise, 2012. http://tel.archives-ouvertes.fr/tel-00809045.
Повний текст джерелаSOAVE, NICOLA. "Variational and geometric methods for nonlinear differential equations." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2014. http://hdl.handle.net/10281/49889.
Повний текст джерелаChen, Huyuan. "Fully linear elliptic equations and semilinear fractionnal elliptic equations." Thesis, Tours, 2014. http://www.theses.fr/2014TOUR4001/document.
Повний текст джерелаThis thesis is divided into six parts. The first part is devoted to prove Hadamard properties and Liouville type theorems for viscosity solutions of fully nonlinear elliptic partial differential equations with gradient term
Zhou, Chiping. "Maximum principles and Liouville theorems for elliptic partial differential equations." Thesis, 1990. http://hdl.handle.net/10125/9958.
Повний текст джерелаHUANG, ZHEN-FANG, and 黃振芳. "Comparison principles and liouville theorems for prescribed mean curvature equations in unbounded domains." Thesis, 1985. http://ndltd.ncl.edu.tw/handle/16276943290704902410.
Повний текст джерелаWu, Mao-ling, and 伍懋靈. "Ambarzumian’s Theorem for the Sturm-Liouville Operator on Graphs." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/46741723810186808370.
Повний текст джерела國立中山大學
應用數學系研究所
95
The Ambarzumyan Theorem states that for the classical Sturm-Liouville problem on $[0,1]$, if the set of Neumann eigenvalue $sigma_N={(npi)^2: nin { f N}cup { 0}}$, then the potential function $q=0$. In this thesis, we study the analogues of Ambarzumyan Theorem for the Sturm-Liouville operators on star-shaped graphs with 3 edges of different lengths. We first solve the direct problem: to find out the set of eigenvalues when $q=0$. Then we use the theory of transformation operators and Raleigh-Ritz inequality to prove the inverse problem. Following Pivovarchik''s work on star-shaped graphs of uniform lengths, we analyze the Kirchoff condition in detail to prove our theorems. In particular, we study the cases when the lengths of the 3 edges satisfy $a_1=a_2=frac{1}{2}a_3$ or $a_1=frac{1}{2}a_2=frac{1}{3}a_3$. Furthermore, we work on Neumann boundary conditions as well as Dirichlet boundary conditions. In the latter case, some assumptions about $q$ have to be made.
Wu, Zhi-Jie, and 吳智傑. "Gradient Estimates for System of Semi-linear Equations and Liouville Theorem." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/00443767841521881320.
Повний текст джерела國立臺灣大學
數學研究所
90
We generalize the results for a scalar equation by Modica to the case of a system of equations. It is shown that if a bounded entire solution U(x) of a system of semi-linear equations satisfies the gradient bound |\nabla U|^{2}\leq 2F(U) for all x\in \Bbb R^{n}, then the Liouville theorem holds. Also we show that the inequality above holds if $F(U)$ satisfies some suitable assumptions.