Boundedness of the gradient of a solution to the Neumann-Laplace problem in a convex domain
Analysis of PDEs
2008-11-07 v2
Abstract
It is shown that solutions of the Neumann problem for the Poisson equation in an arbitrary convex -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.
Keywords
Cite
@article{arxiv.0809.2514,
title = {Boundedness of the gradient of a solution to the Neumann-Laplace problem in a convex domain},
author = {Vladimir Maz'ya},
journal= {arXiv preprint arXiv:0809.2514},
year = {2008}
}