Partial applicability of Moser's method to nonlinear elliptic systems

We consider nonlinear elliptic systems of divergent-type second-order partial differential equations with solutions $u\in W_p^1$. It is proved that $Du\in L_q$ with some $q\in(p;+\infty)$ and it is explicitly shown how $q$ depends on the ellipticity modulus of the system. Some conditions on the ellipticity modulus are obtained under which the solutions satisfy the Hölder conditions and the Liouville theorem holds.