Morrey regularity of solutions of fully non-linear elliptic systems

Let Omega be a bounded convex open set of R-n, n >= 2, of class C-2,C-1. We consider the following Dirichlet problem {u is an element of H-2 boolean AND H-0(1)(Omega, R-N) F(x, D(2)u) = f(x), a.e. in Omega, where f is an element of L-2,L-lambda (Omega, R-N), 0 < lambda < n, and F satisfying the condition A(x). We show that there exists epsilon is an element of (0, 1) such that D(2)u is an element of L-2,L-mu(Omega, R-N), where mu is an element of (0, lambda) and mu < n epsilon.