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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/173459It 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.Analysis of PDEs54C40, 14E20Boundedness of the gradient of a solution to the Neumann-Laplace problem in a convex domaintext