$H^2$ regularity for the $p(x)-$Laplacian in two-dimensional convex domains

Abstract

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 $p_1>1$.

18 pages. Keywords: Variable exponent spaces. Elliptic Equations. $H^2$ regularity

References in corpus (1)

• Interior penalty discontinuous Galerkin FEM for the $p(x)$-Laplacian

Cited by in corpus (2)

• Order of convergence of the finite element method for the $p(x)-$Laplacian
• The decomposition-coordination method for the $p(x)$-Laplacian