Interior regularity of obstacle problems for nonlinear subelliptic systems with VMO coefficients

Abstract This article is concerned with an obstacle problem for nonlinear subelliptic systems of second order with VMO coefficients. It is shown, based on a modification of A-harmonic approximation argument, that the gradient of weak solution to the corresponding obstacle problem belongs to the Morrey space LX,loc2,λ $L_{X,\mathrm{loc}}^{2,\lambda }$.