Lebesgue and Sobolev spaces with variables exponents

Abstract

We studied in this memory the Lebesgue and Sobolev spaces with variable exponents which are a generalizations of the Lebesgue and Sobolev spaces. Our goal from this memory is introduce the Basic elements for this spaces, we give the general definitions for both spaces, the embeddings in Lp(x) and Poincaré inequality in the space Wk,p(x).