Global Regularity in Fractional Order Sobolev Spaces for the p-Laplace Equation on Polyhedral Domains

Abstract

The p -Laplace equation is considered for p > 2 on a n -dimensional convex polyhedral domain under a Dirichlet boundary value condition. Global regularity of weak solutions in weighted Sobolev spaces and in fractional order Nikolskij and Sobolev spaces are proven.