On a nonlinear Robin problem with an absorption term on the boundary and L1 data

We deal with existence and uniqueness of nonnegative solutions to: - {-Delta u=f(x),in Q, partial derivative u/partial derivative nu+lambda(x)u=g(x)/u(eta),on partial derivative Omega, where eta >= 0 and 0 and f , lambda and g are the nonnegative integrable functions. The set Omega subset of R-N(N>2) is open and bounded with smooth boundary, and nu \nu denotes its unit outward normal vector. More generally, we handle equations driven by monotone operators of p p -Laplacian type jointly with nonlinear boundary conditions. We prove the existence of an entropy solution and check that, under natural assumptions, this solution is unique. Among other features, we study the regularizing effect given to the solution by both the absorption and the nonlinear boundary term.