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.
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Carsten Ebmeyer, M. Steinhauer, Wenbin Liu, Global Regularity in Fractional Order Sobolev Spaces for the p-Laplace Equation on Polyhedral Domains. Z. Anal. Anwend. 24 (2005), no. 2, pp. 353–374DOI 10.4171/ZAA/1245