Electron. J. Diff. Equ., Vol. 2011 (2011), No. 62, pp. 1-16.

Quasilinear elliptic problems with nonstandard growth

Mohamed Badr Benboubker, Elhoussine Azroul, Abdelkrim Barbara

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.

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Mohamed Badr Benboubker
University of Fez, Faculty of Sciences Dhar El Mahraz
Laboratory LAMA, Department of Mathematics
B.P 1796 Atlas Fez, Morocco
email: simo.ben@hotmail.com
Elhoussine Azroul
University of Fez, Faculty of Sciences Dhar El Mahraz
Laboratory LAMA, Department of Mathematics
B.P 1796 Atlas Fez, Morocco
email: azroul_elhoussine@yahoo.fr
Abdelkrim Barbara
University of Fez, Faculty of Sciences Dhar El Mahraz
Laboratory LAMA, Department of Mathematics
B.P 1796 Atlas Fez, Morocco
email: abdelkrim.barbara@yahoo.com

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