Renormalized solutions for nonlinear degenerate elliptic problems with \(L^1\) data
The paper deals with the problem of existence of s.c. renormalized solutions for a class of nonlinear degenerate elliptic equations when the left-hand side is represented by the Leray-Lions operator defined on the weighted Sobolev spaces \(W^{1,p}_0(\Omega,w)\), but which is not controlled with respect to the unknown function. Under some assumptions the existence of an at least renormalized solution of the problem, when the solution vanishes on the boundary of an open bounded subset \(\Omega\) of \(\mathbb R^N\), \(N\geq 1\), and the equation right-hand side from \(L^1(\Omega)\), has been proved.
scientific article; zbMATH DE number 5538716