Entropy solutions for the p(x)-Laplace equation

Manel Sanch́on, José Miguel Urbano

Research output: Contribution to journalArticlepeer-review

116 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 languageEnglish (US)
Pages (from-to)6387-6405
Number of pages19
JournalTransactions of the American Mathematical Society
Volume361
Issue number12
DOIs
StatePublished - Dec 1 2009
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics

Fingerprint

Dive into the research topics of 'Entropy solutions for the p(x)-Laplace equation'. Together they form a unique fingerprint.

Cite this