Renormalized solutions for nonlinear degenerate elliptic problems with L1 data

Abstract

We are interested in a class of nonlinear degenerate diffusion problems with a diffusion function a(x, u, Δu) which is not controlled with respect to u and which is not uniformly coercive on the weighted Sobolev spaces W 01,p(Ω, w). Existence of a renormalized solution is proved in the L1-setting.