Title: Weak solutions for some nonlinear elliptic problem with variable exponent and measure data

Authors: Stanislas Ouaro; Safimba Soma

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

Abstract: We prove the existence of weak solutions to nonlinear elliptic equations with variable exponent and measure data. The functional setting involves Lebesgue-Sobolev spaces with variable exponent and Marcinkiewicz spaces.

Keywords: generalised Lebesgue-Sobolev spaces; weak solutions; bounded Radon measure; p(x)-Laplace operators; electrorheological fluids; Marcinkiewicz spaces; nonlinear elliptic problems.

DOI: 10.1504/IJDSDE.2012.045998

International Journal of Dynamical Systems and Differential Equations, 2012 Vol.4 No.1/2, pp.103 - 125

Available online: 19 Mar 2012 *

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