Entropy solutions for the p(x)-Laplace equation

Manel Sanch́on; José Miguel Urbano

doi:10.1090/S0002-9947-09-04399-2

Entropy solutions for the p(x)-Laplace equation

Manel Sanch́on, José Miguel Urbano

Research output: Contribution to journal › Article › peer-review

123 Scopus citations

Abstract

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)
Pages (from-to)	6387-6405
Number of pages	19
Journal	Transactions of the American Mathematical Society
Volume	361
Issue number	12
DOIs	https://doi.org/10.1090/S0002-9947-09-04399-2
State	Published - Dec 1 2009
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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N2 - 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.

AB - 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.

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Entropy solutions for the p(x)-Laplace equation

Abstract

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