On the Regularity of Weak Solutions of Elliptic Systems in Banach Spaces

Abstract

On a domain Ω⊂R^N we consider weak solutions u: Ω→R^Mfor elliptic systems of the kind A(u) + B(u) = f. Here A(u) is a quasilinear elliptic operator of second order satisfying certain structure conditions and B(u) is a perturbation with critical growth in the gradient, i.e. the growth exponent for the gradient p, 1 < p <∞, is the same as the integration exponent of the Sobolev Space W^1,p(Ω) for which (the Nemitzky operator of) A(u)is coercive.