Sobre os espaços de Lebesgue e Sobolev generalizados e aplicações envolvendo o p(x)-laplaciano.

Abstract

In this work we study the spaces Lp(x)() and W1, p(x)(), as well as existence of weak solutions for elliptic problems of type 8<:− p(x)u = f(x, u), x 2, u 2 W1, p(x)(), where RN is a bounded domain or = RN; p(x) > 1 is a continuous function and p(x) denotes p(x)−Laplacian operator, wich is defined by p(x)u = div(|ru|p(x)−2ru). Using variational techniques, we obtain some results of existence of solution for the problems in question.