Nonlinear gradient estimates for elliptic equations of general type

Abstract

We study a very general model of nonvariational elliptic equations of p-Laplacian type. We prove the W 1,q -estimates for each q > p regarding such a nonlinear elliptic equation in divergence form under the assumption that for each point and for each sufficiently small scale the nonlinearity is suitably close to a vector of the gradient in BMO space. In the same spirit our results can be easily extended to Orlicz spaces as well.