CUBO A Mathematical Journal Vol.12, N° 01, (133-148). March 2010

Well-Posedness Results for Anisotropic Nonlinear Elliptic Equations with Variable Exponent and L¹-Data

Stanislas Ouaro

Laboratoire d'Analyse Mathématique des Equations (LAME), UFR. Sciences Exactes et Appliquées, Université de Ouagadougou 03 BP 7021 Ouaga 03 Ouagadougou, Burkina Faso email : souaro@univ-ouaga.bf

ABSTRACT

We study the anisotropic boundary value problem on , where is a smooth open bounded domain in . We prove the existence and uniqueness of an entropy solution for this problem.

Key words and phrases: Anisotropic; variable exponent; entropy solution; electrorheological fluids.

RESUMEN

Estudiamos el problema de valores en la frontera anisotropico en , u = 0 sobre , donde es un dominio abierto suave do . Proveamos la existencia y unicidad de una solución de entropía para este problema.

Math. Subj. Class.: 35J20, 35J25, 35D30, 35B38, 35J60

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 Received: June, 2008.

Revised: november, 2008.