Nonlinear elliptic systems with general growth

We prove local Lipschitz-continuity and, as a consequence, C^kandC^∞regularity of weak solutions u for a class of nonlinear elliptic differential systems of the form . The growth conditions on the dependence of functions on the gradient Du are so mild to allow us to embrace growths between the linear and the exponential cases, and they are more general than those known in the literature.