J. Nonl. Evol. Equ. Appl. 2014 (5), pp. 53-76, published on January 9, 2015:

Entropy solutions for nonlinear nonhomogeneous Neumann problems involving the generalized p(x)-Laplace operator and measure data


M. B. Benboubker

Laboratoire d’Analyse Mathématique et Applications (LAMA), Département de Mathématiques, faculté des Sciences Dhar El Mahraz, B.P 1796 Atlas Fès, Morocco

S. Ouaro

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

U. Traore

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

Received on October 17, 2013
Accepted on April 5, 2014

Communicated by Alexander Pankov

Abstract.  Our aim in this paper is to study the existence of entropy solution for the class of nonlinear p(x)-Laplace problems with Neumann nonhomogeneous boundary conditions and diffuse Radon measure data which does not charge the sets of zero p(.)-capacity.
Keywords:Generalized Sobolev space, Neumann boundary conditions, Entropy solution, Radon measure, p(.)-capacity.
2010 Mathematics Subject Classification:   35J20, 35J25, 35D30, 35B38, 35J60.

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