Full paper in PDF format:
$%L. Aharouch, J. Bennouna, and A. Touzani, Existence of renormalized solution of some elliptic problems in Orlicz spaces, Rev. Mat. Complut. 22 (2009), no. 1, 91–110.%$

Existence of Renormalized Solution of Some Elliptic Problems in Orlicz Spaces

Lahsen AHAROUCH, Jaouad BENNOUNA,
and Abdelfettah TOUZANI

Faculté polydisciplinaire Ouarzazate BP 638 Ouarzazate — Morocco laharouch@gmail.com	Département de Mathématiques et Informatique Faculté des Sciences Dhar-Mahraz B.P 1796 Atlas Fès — Morocco jbennouna@hotmail.com atouzani@menara.ma

Received: January 18, 2007
Accepted: January 24, 2008

ABSTRACT

In this paper, we study the problem

- diva(x,u,∇u )- div ϕ(u)+ g(x,u) = f

in the framework of Orlicz spaces. The main contribution of our work is to prove the existence of a renormalized solution without any restriction on the $N$ -function of the Orlicz space.

Key words: Orlicz Sobolev spaces, boundary value problems, truncations, renormalized solutions.
2000 Mathematics Subject Classification: 35J60.