Regularity of Weak Solutions of Nonlinear Equations with Discontinuous Coefficients

In this paper, we prove that the weak solutions uW1,ploc()(1>p>) of the following equation with vanishing mean oscillation coefficients A(x): div[(A(x)uu)p22A(x)u*|F(x)|p2F(x)]=B(x,u,u), belong to W1,qloc()(q(p,)), provided FLqloc() and B(x, u, h) satisfies proper growth conditions, where R N (N 2) is a bounded open set, A(x) = (A ij(x)) NN is a symmetric matrix function.