Regularity of weak solutions to obstacle problems for nondiagonal quasilinear degenerate elliptic systems

Let X={X1, ... ,Xm} be a system of smooth real vector fields satisfying Hormander's rank condition. We consider the interior regularity of weak solutions to an obstacle problem associated with the nonhomogeneous nondiagonal quasilinear degenerate elliptic system X alpha* (A(ij)(alpha beta) (x, u)X(beta)u(j)) = B-i( x, u, Xu) + X-alpha*g(i)(alpha) (x, u, Xu). After proving the higher integrability and a Campanato type estimate for the weak solutions to the obstacle problem for the homogeneous nondiagonal quasilinear degenerate elliptic system, the interior Morrey regularity and Holder continuity of weak solutions to the obstacle problem for the nonhomogeneous system are obtained.