Nonlinear anisotropic elliptic and parabolic equations with variable exponents and $L^1$ data

Mostafa Bendahmane; Kenneth Hvistendahl Karlsen; Mazen Saad

doi:10.3934/cpaa.2013.12.1201

Article Contents

2013, Volume 12, Issue 3: 1201-1220. Doi: 10.3934/cpaa.2013.12.1201

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Nonlinear anisotropic elliptic and parabolic equations with variable exponents and $L^1$ data

1.
Université Victor Ségalen - Bordeaux 2, 146 rue Léo Saignat, BP 26, 33076 Bordeaux
2.
Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, NO-0316 Oslo
3.
Ecole Centrale de nantes, Laboratoire de Mathématiques Jean Leray, UMR CNRS 6629, 1, rue de la Noé, 44321 Nantes

Received: August 31, 2011

Revised: July 31, 2012

Published: April 2013

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Abstract

We prove existence and regularity results for distributional solutions of nonlinear elliptic and parabolic equations with general anisotropic diffusivities with variable exponents. The data are assumed to be merely integrable.

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Mathematics Subject Classification: 35J60, 35K55, 35D10.

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