Nonlinear elliptic systems with general growth

Abstract

We prove local Lipschitz-continuity and, as a consequence, C k and C ∞ regularity of weak solutions u for a class of nonlinear elliptic differential systems of the form ∑ i = 1 n ∂ ∂ x i a i α ( Du ) = 0 , α = 1 , 2 , … , m . The growth conditions on the dependence of functions a i α ( · ) 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.