Regularity results for solutions of nonlinear elliptic equations with L1,λ data

We consider the Dirichlet problem associated with equations whose prototype is -Delta(p)u = f in Omega where Omega subset of R-n, n >= 3, P is an element of [2, n[, -Delta(p) is the p-Laplacian operator and f belongs to the Morrey spate L-1,L-lambda(Omega) with lambda is an element of]0, n-p]. Firstly, we prove that the gradient of the truncation T-j(u) belongs to L-loc(p,lambda) (Omega) for all j > 0 and, as a consequence, we establish regularity results in suitable weak Morrey spaces for u and its gradient. (C) 2007 Elsevier Ltd. All rights reserved.