$H^2$ regularity for the $p(x)-$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 $p:\Omega \to [p_1,\infty)$ with $p\in Lip(\bar{\Omega})$ and $p_1>1$. 
Leandro M. Del Pezzo and Sandra Martinez
math.AP