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.