Renormalized solutions for a p(·)-Laplacian equation with Neumann nonhomogeneous boundary condition involving diffuse measure data and variable exponent

Abstract

Abstract In this paper we prove the existence of at least one renormalized solution for the p(x)-Laplacian equation associated with a maximal monotone operator and Radon measure data. The functional setting involves Sobolev spaces with variable exponent W1,p(·)(Ω).