# name
Entropy solutions for the $p(x)$-Laplace equations

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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 $ 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.

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Transactions of the American Mathematical Society, 2009, vol. 361, num. 12, p. 6387-6405

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(c) American Mathematical Society (AMS), 2009

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Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Entropy solutions for the $p(x)$-Laplace equations