regularity for the -Laplacian in two-dimensional convex domains

In this paper we study the H 2 global regularity for solutions of the p ( x ) -Laplacian in two-dimensional convex domains with Dirichlet boundary conditions. Here p : Ω → [ p 1 , ∞ ) with p ∈ Lip ( Ω ¯ ) and p 1 > 1 .