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 non-linear elliptic systems under the natural growth condition.We obtain a general criterion for a weaksolution to be regular in the neighborhood of a given boundary point.The proof yields directly theoptimal regularity for the solution in this neighborhood.This result is new for the situation under thenatural growth conditions.