Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 62, pp. 1-16.

Title: Quasilinear elliptic problems with nonstandard growth
       
Author: Mohamed Badr Benboubker (Univ. of Fez, Morocco)
        Elhoussine Azroul  (Univ. of Fez, Morocco)
	Abdelkrim Barbara  (Univ. of Fez, Morocco)

Abstract:
 We prove the existence of solutions to Dirichlet problems
 associated with the $p(x)$-quasilinear elliptic equation
 $$
 Au =- \hbox{div} a(x,u,\nabla u)= f(x,u,\nabla u).
 $$
 These solutions are obtained in Sobolev spaces with
 variable exponents.

Submitted November 1, 2010. Published May 11, 2011.
Math Subject Classifications: 35J20, 35J25.
Key Words: Quasilinear elliptic equation;
           Sobolev spaces with variable exponent;
           image processing; Dirichlet problem.