Estimates for the Gradient of Solutions of Nonlinear Elliptic Equations with L1 Data

Abstract

We prove estimates for the gradient of solutions u of the homogeneous Dirichlet problem for an equation in the form A(u) =f, where A(u) is a p-laplacian type operator and fis a summable function. The estimate on \Du\ is obtained via an estimate on its rearrangement.