The method of A-harmonic approximation and boundary regularity for nonlinear elliptic systems under the natural growth condition

We consider the questions of boundary regularity for weak solutions of second-order nonlinear elliptic systems under the natural growth condition. We obtain a general criterion for a weak solution to be regular in the neighborhood of a given boundary point. The proof yields directly the optimal regularity for the solution in this neighborhood. This result is new for the situation under the natural growth conditions. Supported by NSF(No. 10531020) of China and the Program of 985 Innovation Engineering on Information in Xiamen University (2004–2007) and NCETXMU