Boundedness of the gradient of a solution to the Neumann-Laplace problem in a convex domain

Vladimir Maz'ya

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arXiv · 0809.2514

Boundedness of the gradient of a solution to the Neumann-Laplace problem in a convex domain

Vladimir Maz'ya

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Abstract

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.

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Vladimir Maz'ya. 2008-11-07. Boundedness of the gradient of a solution to the Neumann-Laplace problem in a convex domain. https://arxiv.org/abs/0809.2514

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