# REGULARITE EN CALCUL DES VARIATIONS. ESPACES DE SOBOLEV FRACTIONNAIRES.

Abstract : In this thesis, we address several questions in the calculus of variations and in the theory of elliptic partial differential equations.
In chapter 1, we consider the lower bounded slope condition for maps defined on the boundary of an open set in $\R^n.$
In chapter 2, we consider the problem to minimize $u\mapsto \int\{ F(\nabla u(x))+G(x,u(x))\}\,dx$ where the boundary condition is given by a function which satisfies a lower bounded slope condition.
In chapter 3, we consider a nonlinear elliptic partial differential equation with a boundary condition which satisfies a lower bounded slope condition.
In chapter 4, we give a description of the connected components of $W^{s,p}(M,N).$
In chapter 5, we identify the singular set of a map $u\in W^{s,p}(S^N,S^1).$
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Theses
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Cited literature [19 references]

https://tel.archives-ouvertes.fr/tel-00119614
Contributor : Pierre Bousquet <>
Submitted on : Monday, December 11, 2006 - 4:45:47 PM
Last modification on : Wednesday, July 8, 2020 - 12:43:13 PM
Long-term archiving on: : Tuesday, April 6, 2010 - 8:49:29 PM

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• HAL Id : tel-00119614, version 1

### Citation

Pierre Bousquet. REGULARITE EN CALCUL DES VARIATIONS. ESPACES DE SOBOLEV FRACTIONNAIRES.. Mathématiques [math]. Université Claude Bernard - Lyon I, 2006. Français. ⟨tel-00119614⟩

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