Regularity results for the gradient of solutions of linear elliptic systems with VMO-coefficients and L^{1,lambda} data

We prove that if a vector-function f belongs to the Morrey space L(1,lambda)(Omega, R(N)), with Omega subset of R(n), n >= 3, N >= 2, lambda is an element of [0, n - 2], then there exists a very weak solution u of the system{-D(i) (A(ij) (x) D(j) u) = f in ohmu is an element of W(0)(1,1)(ohm,R(N))such that Du belongs to the space L(loc)(q,n-q(n-lambda-1)) (ohm,R(nN)) for any q is an element of [1, n/n-1 [ provided the matrix of coefficients (A(ij)) has L(infinity) VMO entries.