We consider a Dirichlet problem in divergence form with variable growth, modeled on the p(x)-Laplace equation. We obtain existence and uniqueness of an entropy solution for L1 data, as well as integrability results for the solution and its gradient. The proofs rely crucially on a priori estimates in Marcinkiewicz spaces with variable exponent, for which we obtain new inclusion results of independent interest. © 2009 American Mathematical Society.
ASJC Scopus subject areas
- General Mathematics