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.
|Original language||English (US)|
|Number of pages||19|
|Journal||Transactions of the American Mathematical Society|
|State||Published - Dec 1 2009|
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