English

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 nn-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}
}