BMO estimate to A-harmonic systems with discontinuous coefficients

In this note, we prove a global BMO estimate of the gradient of each weak solution to a class of nonlinear degenerate elliptic system with leading coefficients satisfying vanishing means oscillations. This conclusion perfects nonlinear Calderón–Zygmund theory in the limiting case to certain degenerate elliptic system. As an application of the BMO estimate, we give another proof to its LpLp theory with 1