Boundary higher integrability for the gradient of distributional solutions of nonlinear systems

We consider distributional solutions to the Dirichlet problem for nonlinear elliptic systems of the type {div A(x, u, Du) = div f in Omega, u - u(0) is an element of W-0(1,r)(Omega), with r less than the natural exponent p which appears in the coercivity and growth assumptions for the operator A. We prove that Du is an element of W-1,W-p(Omega) if \r - p\ is small enough.