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Weighted Sobolev spaces and nonhomogeneous elliptic problems in the half-space

Abstract : The aim of this PhD thesis is the solution of some elliptical problems in the half-space. Using the results on the Dirichlet and Neumann problems for the Laplace operator in this geometry, we have explored various aspects of the biharmonic and Stokes problems. We give existence, uniqueness and regularity fundamental results. For that, we consider data and give solutions which live in weighted Sobolev spaces. We assume that the boundary conditions are nonhomogeneous and we also take them in weighted Sobolev spaces. An important aspect of this study is the case of singular boundary conditions and the very weak solutions which correspond to it. We also treat the question of non standard boundary conditions, in particular the Navier conditions for the Stokes problem.
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Contributor : Yves Raudin <>
Submitted on : Monday, March 3, 2008 - 7:11:42 PM
Last modification on : Friday, January 15, 2021 - 9:24:19 AM
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  • HAL Id : tel-00260327, version 1



Yves Raudin. Weighted Sobolev spaces and nonhomogeneous elliptic problems in the half-space. Mathematics [math]. Université de Pau et des Pays de l'Adour, 2007. English. ⟨tel-00260327⟩



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