Entropy and renormalized solutions for the p(x)-laplacian equation with measure data

Abstract

In this paper we prove the existence and uniqueness of both entropy solutions and renormalized solutions for the p(x)-Laplacian equation with variable exponents and a signed measure in L 1(Ω)+W -1,p′(⋅)(Ω). Moreover, we obtain the equivalence of entropy solutions and renormalized solutions.