Comptes Rendus
no. 9-10
Partial Differential Equations/Harmonic Analysis
Boundedness of the gradient of a solution to the Neumann–Laplace problem in a convex domain
[Bornitude du gradient d'une solution du problème de Neumann pour le Laplacien dans un domaine convexe]

Présenté par : Evariste Sanchez-Palencia

Vladimir Maz'ya1, 2
1 Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK
2 Department of Mathematics, Linköping University, Linköping, 581 83, Sweden
Comptes Rendus. Mathématique, Volume 347 (2009) no. 9-10, pp. 517-520.

On démontre que les solutions du problème de Neumann pour l'équation de Poisson dans un domaine convexe arbitraire de dimension n sont uniformément Lipschitz. Les applications de ce résultat à quelques aspects de régularité de solutions du problème de Neumann sur les polyèdres convexes sont données.

It is shown that solutions of the Neumann problem for the Poisson equation in an arbitrary convex n-dimensional domain are uniformly Lipschitz. Applications of this result to some aspects of regularity of solutions to the Neumann problem on convex polyhedra are given.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.03.001

Vladimir Maz'ya 1, 2

1 Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK
2 Department of Mathematics, Linköping University, Linköping, 581 83, Sweden 
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Vladimir Maz'ya. Boundedness of the gradient of a solution to the Neumann–Laplace problem in a convex domain. Comptes Rendus. Mathématique, Volume 347 (2009) no. 9-10, pp. 517-520. doi : 10.1016/j.crma.2009.03.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.03.001/

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