Regularity for systems and the angle condition.

Abstract

In this dissertation we consider weak solutions of the System A(u) + B(u) = 0 on a bounded domain W⊂ Rn where B(u) is a perturbation of critical growth, i.e. its growth exponent p equals the integrability exponent of the Sobolev space for which A(u) is a coercive elliptic operator. Under certain structure conditions we get a higher integrability result for 1 < p < n and a regularity result for p > 2.