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

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

2008-09-15

arxiv.org/abs/0809.2514v2

Mathematics

Analysis of PDEs

Scientific paper

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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