Dissertations / Theses on the topic 'Minimal surface equation'
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Krust, Romain. "Le problème de Dirichlet pour l' équation des surfaces minimales." Paris 7, 2005. http://www.theses.fr/1992PA077323.
Full textMelin, Jaron Patric. "Examples of discontinuity for the variational solution of the minimal surface equation with Dirichlet data on a domain with a nonconvex corner and locally negative mean curvature." Thesis, Wichita State University, 2013. http://hdl.handle.net/10057/10639.
Full textThesis (M.S.)--Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics, Statistics, and Physics
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.
Full textPagliardini, Dayana. "Fractional minimal surfaces and Allen-Cahn equations." Doctoral thesis, Scuola Normale Superiore, 2018. http://hdl.handle.net/11384/85738.
Full textBäck, Per. "Bäcklund transformations for minimal surfaces." Thesis, Linköpings universitet, Matematik och tillämpad matematik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-119914.
Full textMazet, Laurent. "Construction de surfaces minimales par résolution du problème de Dirichlet." Phd thesis, Université Paul Sabatier - Toulouse III, 2004. http://tel.archives-ouvertes.fr/tel-00007780.
Full textRodiac, Rémy. "Méthodes variationnelles pour des problèmes sous contrainte de degrés prescrits au bord." Thesis, Paris Est, 2015. http://www.theses.fr/2015PESC1108/document.
Full textThis thesis is devoted to the mathematical analysis of some variational problems. These problem sare motivated by the Ginzburg-Landau model related to the super conductivity. In the first part we study existence of solutions of the Ginzburg-Landau equations without magnetic eld but with semi-sti boundary conditions. These conditions are obtained by prescribing the modulus of the function on the boundary of the domain along with its topological degree. This is a particular case of free boundary problems, where the function on the boundary is an unknown of the problem. Existence of solutions of that problem does not necessary hold. Indeed we can not apply the direct method of the calculus of variations since the degree on the boundaryis not continuous with respect to the weak convergence in an appropriated Sobolev space. This is problem with loss of compactness. By studying the bublling" phenomenon which come upin such problems we obtain some existence and non existence results .In Chapter 1 we study conditions under which the dierence between two energy levels is strictly optimal. In order to do that we adapt a technique due to Brezis-Coron. This allow us to recover known existence results (previously obtained by Berlyand and Rybalko and DosSantos) for stable solutions of the Ginzburg-Landau equations in multiply connected domains. In Chapter 2 we are interested in harmonic maps with values in $R^2$ with prescribed degree boundary condition in an annulus. We make a link between this problem and the minimal surface theory in $R^3$ thanks to the so-called Hopf quadratic differential. This leads us to study immersed minimal surfaces bounded by two circles in parallel planes. We prove the existence of such surfaces die rent from catenoids by using a bifurcation argument. We then apply the results obtained to deduce existence and non existence results for minimizers of the Ginzburg-Landau energy with prescribed degrees. This is done in Chapter 3 where the results are obtained for large ".Chapter 4 is devoted to prescribed degree problems in dimension n3 . We prove the non existence of minimizers of the Ginzburg-Landau energy in simply connected domains. We then study min-max critical points of a perturbed energy. The second part is devoted to the asymptotic analysis of solutions of the Ginzburg-Landau equations when "goes to zero. Sandier and Serfaty studied the asymptotic behavior of the vorticity measures associated to these equations. They derived critical conditions on the limiting measures both with and without magnetic Field. We are interested by these conditions when there is no magnetic Field. The problem of the local regularity of the limiting measures is then equivalent to the study of regularity of stationary harmonic functions whose Laplacianis a measure. We show that locally such measures are concentrated on a union of lines which belong to the zero set of an harmonic function
Melo, Marcos Ferreira de. "ImersÃes isomÃtricas em grupos de Lie nilpotentes e solÃveis." Universidade Federal do CearÃ, 2008. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=5541.
Full textConselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico
Neste trabalho, demonstramos teoremas estabelecendo condiÃÃes suficientes para a existÃncia de imersÃes isomÃtricas com curvatura extrÃnseca prescrita em grupos de Lie nilpotentes e solÃveis. Obtemos assim uma generalizaÃÃo do Teorema Fundamental da Teoria de Subvariedades em Rn e, em particular, obtemos resultados de imersÃo em todos os grupos tipo-Heisenberg e em todos os espaÃos de Damek-Ricci.
In this paper, we prove theorems establishing sufficient conditions to existence for isometric immersions with prescribed extrinsic curvature in two-step nilpotent Lie groups and solvmanifolds. We obtain a generalization of the Fundamental Theorem of Submanifold Theory in Rn and, in particular, we one has immersion results in the generally Heisenberg type groups and Damek-Ricci spaces.
Wuttke, Sebastian. "Some aspects of the Wilson loop." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2015. http://dx.doi.org/10.18452/17225.
Full textThis thesis is motivated by the AdS/CFT correspondence and the duality between gluon scattering amplitudes and light-like polygonal Wilson loops in N=4 super Yang-Mills theory. At strong coupling light-like polygonal Wilson loops and gluon scattering amplitudes have a description in terms of space-like minimal surfaces in AdS5. We use a Pohlmeyer reduction to derive a classification of all space-like minimal surfaces in AdS3xS3 that have flat projections. The classification consists of nine different classes and contains space-like, time-like and degenerated AdS3 projections. For solutions that admit a closed light-like polygonal boundary we calculate the regularized area. At weak coupling light-like polygonal Wilson loops and gluon scattering amplitudes obey the BDS Ansatz corrected by a remainder function. We present a renormalisation group equation technique using self-crossing Wilson loops to extract the divergences of the remainder function in this limit. Using this technique we analyse two different types of self-crossing. We present the leading and sub-leading divergences up to four loops for a crossing between two edges and the leading divergences for a crossing between two vertices. For a crossing between two edges we present an analytic continuation to the euclidean regime to predict certain terms that have to occur in the unknown analytic expression of the remainder function.
Li, Jin Chuan, and 李金川. "Some uniqueness theorems for the minimal surface equation on an unbounded domain in R2." Thesis, 1995. http://ndltd.ncl.edu.tw/handle/83646109159180482059.
Full textTsai, Bing-Kun, and 蔡秉昆. "On the Uniqueness of Minimal Surface Equation in an Infinite Sector Domainwith Capillary Boundary Condition." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/42474911736552288301.
Full text國立臺灣大學
數學研究所
96
We consider the minimal surface equation in an infinite sector domain with given capillary boundary conditions.First, we give a necessary and sufficient conditions for the existence of the linear solution. Second, we study the behavior of the solutions of the minimal surface equation at the origin and at the infinite by using the blow up and the sip in process. Finally, we claim that the solution is linear on the boundary and conclude that it is a plane.
Tsai, Bing-Kun. "On the Uniqueness of Minimal Surface Equation in an Infinite Sector Domain with Capillary Boundary Condition." 2008. http://www.cetd.com.tw/ec/thesisdetail.aspx?etdun=U0001-2407200811150700.
Full textAdams, David. "Rates of asymptotic convergence for solutions of geometric variational problems." Phd thesis, 1986. http://hdl.handle.net/1885/138468.
Full textTorres, Mónica. "Plane-like minimal surfaces in periodic media with inclusions." Thesis, 2002. http://hdl.handle.net/2152/999.
Full textTorres, Monica. "Plane-like minimal surfaces in periodic media with inclusions." 2002. http://wwwlib.umi.com/cr/utexas/fullcit?p3086718.
Full textGuillen, Nestor Daniel. "Regularization in phase transitions with Gibbs-Thomson law." Thesis, 2010. http://hdl.handle.net/2152/ETD-UT-2010-12-2562.
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Maringová, Erika. "Eliptické rovnice v nereflexivních prostorech funkcí." Master's thesis, 2015. http://www.nusl.cz/ntk/nusl-347207.
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