2004-Fez conference on Differential Equations and Mechanics. Electron. J. Diff. Eqns., Conference 11, 2004, pp. 1-10.

Existence and regularity of entropy solutions for some nonlinear elliptic equations

Lahsen Aharouch, Elhoussine Azroul

Abstract:
This paper concerns the existence and regularity of entropy solutions to the Dirichlet problem
$$\displaylines{ Au = -\mathop{\rm div} (a(x, u, \nabla u)) = f - \mathop{\rm div}\phi(u) \quad \hbox{in }\Omega \cr u = 0 \quad \hbox{on } \partial \Omega. }$$
In particular, we show the $L^{{\bar q}}$-regularity of the solution to this boundary-value problem.

Published October 15, 2004.
Math Subject Classifications: 35J60.
Key Words: Orlicz Sobolev spaces; boundary value problems; Entropy solution.

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Lahsen Aharouch
Département de Mathéematiques et Informatique
Faculté des Sciences Dhar-Mahraz
B.P. 1796 Atlas Fès, Maroc
email: lahrouche@caramail.com
Elhoussine Azroul
Département de Mathéematiques et Informatique
Faculté des Sciences Dhar-Mahraz
B.P. 1796 Atlas Fès, Maroc
email: elazroul@caramail.com

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