Regularity results for the gradient of solutions of a class of linear elliptic systems with L^{1,λ} data

We prove that if a vector-function f belongs to the Morrey space L-1,L-lambda(Omega, R-N), with Omega subset of R-n, n >= 3, N >= 2, lambda epsilon|0, n - 2|, and u is the solution of the system{-D-i(A(ij)(x)D-ju) = f in Omega u epsilon W-0(1,1) (Omega, R-N)then Du belongs to the space L-q,L-n-q(n-lambda-1)(Omega, R-nN), for any q epsilon [1, n/n-1[, provided the matrix of bounded measurable coefficients (A(ij)) has sufficiently small dispersion of the eigenvalues. (C) 2007 Elsevier Ltd. All rights reserved.