# Quelques méthodes de résolution d'équations aux dérivées partielles elliptiques avec contrainte sur les espaces $W^{1, p}$ et $BV$.

Abstract : This thesis deals with some singular and degenerated partial differential equations with constraint. We also consider some equations, called penalized equations, where the constraint is replaced with a term tending asymptotically towards the constraint.
This allows us to obtain a more flexible numerical approximation of the initial partial differential equation with constraint.
The first part of this thesis, which deals with the approximation of the first eigenvalue of the 1-Laplacian operator, has been accepted for publication in the journal Annales de la Faculté des Sciences de Toulouse.
In the second part, our results about the obstacle problem on $W_p^{0, 1}$, $p> 1$ , generalize Adams and Lenhart's results obtained for the case $p =2$.
Namely, we prove existence and uniqueness of a solution of the considered obstacle problem.
The last part, which is the subject of a forthcoming paper, deals with an obstacle problem on $W_1^{0,1}$, which leads us to introduce the space $BV$.
The employed methods come from variational calculus, the theory of measured derivatives functions, vague topology, measure tight topology, convexity, duality theory, approximation and so on.
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Theses
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https://tel.archives-ouvertes.fr/tel-00134253
Contributor : Mouna Kraiem <>
Submitted on : Thursday, March 1, 2007 - 11:38:01 AM
Last modification on : Monday, January 25, 2021 - 2:36:02 PM
Long-term archiving on: : Tuesday, April 6, 2010 - 10:05:58 PM

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• HAL Id : tel-00134253, version 1

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Mouna Kraiem. Quelques méthodes de résolution d'équations aux dérivées partielles elliptiques avec contrainte sur les espaces $W^{1, p}$ et $BV$.. Mathématiques [math]. Université de Cergy Pontoise, 2006. Français. ⟨tel-00134253⟩

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