The Method of A-Harmonic Approximation and Optimal Interior Partial Regularity for Nonl inear Ell iptic Systems Under Controllable Growth Conditions

摘要

In this paper , we consider the nonlinear elliptic systems under the controllable g rowthcondition. We use a new method introduced by Duzaar and Grotowski, for proving partial r egularit yfor weak solutions, based on a generalization of the technique of harmonic approximation. We ex tendprevious partial regularity results under the natural growth condition to the case of the contr ollablegr ow th condition, and establishing the optimal Holder exponent for the derivativ e of a weak solutiondirectly .