Full paper in PDF format:
$%K. Ammar and H. Redwane, Renormalized solutions for nonlinear degenerate elliptic problems with L¹data, Rev. Mat. Complut. 22 (2009), no. 1, 37–52.%$

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 ammar@math.tu-berlin.de	Faculté des Sciences Juridiques Economiques et Sociales Université Hassan 1 B.P. 784. Settat — Morocco redwane_hicham@yahoo.fr

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

ABSTRACT

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.