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

2008/09/15 by Vladimir Maz’ya, Maz'ya, Vladimir
Computer Science · Mathematics · #14E20 #54C40 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.0809.2514

openalex publication_date 2008/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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