Existence of entropy solutions for degenerate quasilinear elliptic equations in \(L^1\) (Q2925405)

The author is concerned with the study of entropy solutions for the degenerate elliptic problem NEWLINE\[NEWLINE-\text{div}[\omega(x)A(x,u,\nabla u)]=f(x)-\text{div}(G),NEWLINE\]NEWLINE in \(\Omega\), subject to homogeneous Dirichlet boundary condition on \(\partial\Omega\). Here \(\Omega\) is a bounded open set in \({\mathbb R}^N \), \(N\geq 2\), \(f\in L^1(\Omega)\), \(G/\omega\in L^{p'}(\Omega,\omega)^N\). The main result of the paper establishes the existence of an entropy solution under standard hypotheses on the functions \(A\) and \(f\). The approach is variational and uses an approximation argument.