Bounds for the singular set of solutions to non linear elliptic systems

We give new estimates for the Hausdorff dimension of the singular set of solutions to elliptic systems - div a(x,u,Du) = b(x,u,Du). If the vector fields a and b are Holder continuous with respect to the variables (x,u) with exponent alpha, then, under suitable assumptions, the Hausdorff dimension of the singular set of any weak solution is at most n-2alpha. We consider natural growth assumptions on a(x,u,Du) with respect to u and critical ones on the right hand side b(x,u,Du), with respect to Du.