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International Journal of Differential Equations
Volume 2013, Article ID 476781, 14 pages
http://dx.doi.org/10.1155/2013/476781
Research Article

Entropy Solutions for Nonlinear Elliptic Anisotropic Homogeneous Neumann Problem

Laboratoire d'Analyse Mathématique des Equations (LAME), UFR, Sciences Exactes et Appliquées, Université de Ouagadougou, 03 BP 7021 Ouaga 03, Ouagadougou, Burkina Faso

Received 22 June 2012; Accepted 1 February 2013

Academic Editor: Elena Braverman

Copyright © 2013 B. K. Bonzi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We prove the existence and uniqueness of entropy solution for nonlinear anisotropic elliptic equations with Neumann homogeneous boundary value condition for -data. We prove first, by using minimization techniques, the existence and uniqueness of weak solution when the data is bounded, and by approximation methods, we prove a result of existence and uniqueness of entropy solution.