Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 68, pp. 1-27.
Title: Existence and regularity of entropy solutions for strongly
nonlinear p(x)-elliptic equations
Authors: Elhoussine Azroul (Univ. of Fez, Morocco)
Hassane Hjiaj (Univ. of Fez, Morocco)
Abdelfattah Touzani (Univ. of Fez, Morocco)
Abstract:
This article is devoted to study the existence of solutions for
the strongly nonlinear p(x)-elliptic problem
$$\displaylines{
- \operatorname{div} a(x,u,\nabla u) + g(x,u,\nabla u)
= f- \operatorname{div} \phi(u) \quad \text{in } \Omega, \cr
u = 0 \quad \text{on } \partial\Omega,
}$$
with $ f\in L^1(\Omega) $ and $ \phi \in C^{0}(\mathbb{R}^{N})$,
also we will give some regularity results for these solutions.
Submitted May 22, 2012. Published March 08, 2013.
Math Subject Classifications: 35J20, 35J25, 35J60.
Key Words: Sobolev spaces with variable exponents; entropy solutions;
strongly nonlinear elliptic equations; boundary value problems.