Boundedness of the gradient of a solution to the Neumann-Laplace problem in a convex domain
Vladimir Gilelevich Maz'ya · arXiv (Cornell University) · 2008
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.