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ISSN 1088-6850(e) ISSN 0002-9947(p)

Entropy solutions for the -Laplace equation

Author(s): Manel Sanchón; José Miguel Urbano
Journal: Trans. Amer. Math. Soc. 361 (2009), 6387-6405.
MSC (2000): Primary 35J70; Secondary 35D05, 35D10, 46E35
Posted: June 18, 2009
MathSciNet review: 2538597
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: We consider a Dirichlet problem in divergence form with variable growth, modeled on the -Laplace equation. We obtain existence and uniqueness of an entropy solution for 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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