Existence of a renormalized solution of nonlinear degenerate elliptic problems
Volume 41 / 2014
Applicationes Mathematicae 41 (2014), 131-140
MSC: Primary 35J70; Secondary 35J85.
DOI: 10.4064/am41-2-1
Abstract
We study a general class of nonlinear elliptic problems associated with the differential inclusion $\beta (u)-{\rm div}(a(x,Du)+F(u))\ni f $ in $\varOmega $ where $f\in L^{\infty }(\varOmega )$. The vector field $a(\cdot ,\cdot )$ is a Carathéodory function. Using truncation techniques and the generalized monotonicity method in function spaces we prove existence of renormalized solutions for general $L^\infty $-data.
