Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 16 (2009), No. 2, 523--541Copyright Heldermann Verlag 2009 Weak and Entropy Solutions to Nonlinear Elliptic Problems with Variable Exponent Stanislas Ouaro Laboratoire d'Analyse Mathématique des Equations, Institut des Sciences Exactes et Appliquées, Université de Ouagadougou, 03 BP 7021 Ouaga 03, Ouagadougou, Burkina Faso souaro@univ-ouaga.bf Sado Traore Laboratoire d'Analyse Mathématique des Equations, Institut des Sciences Exactes et Appliquées, Université de Bobo Dioulasso, 01 BP 1091, Bobo-Dioulasso 01, Burkina Faso sado@univ-ouaga.bf [Abstract-pdf] We study the boundary value problem $-div(a(x,\nabla u))=f(x,u)$ in $\Omega$, $u=0$ on $\partial \Omega$, where $\Omega$ is a smooth bounded domain in $\mathbb{R}^{N}$ and $div(a(x,\nabla u))$ is a $p(x)$-Laplace type operator. We obtain the existence and uniqueness of an entropy solution for $L^{1}$-data $f$ independent of $u$, the existence of weak energy solution for general data $f$ dependent of $u$ where the variable exponent $p(.)$ is not necessarily continuous. Keywords: Generalized Lebesgue-Sobolev spaces, weak energy solution, entropy solution, p(x)-Laplace operator, electrorheological fluids. [ Fulltext-pdf  (177  KB)] for subscribers only.