Sanchón, ManelUrbano, José Miguel2016-03-142016-03-142009-120002-9947https://hdl.handle.net/2445/96448We 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 $ L^1$ 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.19 p.application/pdfeng(c) American Mathematical Society (AMS), 2009Equacions en derivades parcialsOperadors el·lípticsAnàlisi funcional no linealPartial differential equationsElliptic operatorNonlinear functional analysisinfo:eu-repo/semantics/article5697212016-03-14info:eu-repo/semantics/openAccess