2004-Fez conference on Differential Equations and Mechanics.
Electronic Journal of Differential Equations,
Conference 11, 2004, pp. 1-10.
Title: Existence and regularity of entropy solutions for some
nonlinear elliptic equations
Authors: Lahsen Aharouch (Faculte des Sciences Dhar-Mahraz, Maroc)
Elhoussine Azroul (Faculte des Sciences Dhar-Mahraz, Maroc)
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.