Regularity for weak solutions to nondiagonal quasilinear degenerate elliptic systems

The aim of this paper is to establish regularity for weak solutions to the nondiagonal quasilinear degenerate elliptic systems related to Hormander's vector fields, where the coefficients are bounded with vanishing mean oscillation. We first prove L-p (p >= 2) estimates for gradients of weak solutions by using a priori estimates and a known reverse Holder inequality, and consider regularity to the corresponding nondiagonal homogeneous degenerate elliptic systems. Then we get higher Morrey and Campanato estimates for gradients of weak solutions to original systems and Holder estimates for weak solutions. (C) 2016 Elsevier Inc. All rights reserved.