Full paper in PDF format:
$%K. Ammar and H. Redwane, Renormalized solutions for  nonlinear degenerate elliptic problems with L1 data, Rev. Mat. Complut. 22 (2009), no. 1, 37–52.%$

Renormalized Solutions for
Nonlinear Degenerate Elliptic Problems
with L1 Data
Kaouther AMMAR and Hicham REDWANE
TU Berlin
Institut für Mathematik, MA 6-3
Strasse des 17. Juni 136
10623 Berlin — Germany

Faculté des Sciences Juridiques
Economiques et Sociales
Université Hassan 1
B.P. 784. Settat — Morocco


Received: August 27, 2007
Accepted: January 29, 2008


We are interested in a class of nonlinear degenerate diffusion problems with a diffusion function a(x,u,∇u )  which is not controlled with respect to u  and which is not uniformly coercive on the weighted Sobolev spaces   1,p
W 0 (Ω,w)  . Existence of a renormalized solution is proved in the  1
L  -setting.

Key words: Renormalized solutions, nonlinear degenerate elliptic equations, weighted Sobolev spaces.
2000 Mathematics Subject Classification:
47A15, 46A32, 47D20.