On the spaces Lp(x)(Ω) and Wm,p(x)(Ω)1

Abstract

In this paper we present some basic results on the generalized Lebesgue spaces Lp(x)(Ω) and generalized Lebesgue-Sobolev spaces Wm,p(x)(Ω). These results provide the necessary framework for the study of variational problems and elliptic equations with non-standard p(x)-growth conditions. © 2001 Academic Press.