THE PHI-HARMONIC APPROXIMATION AND THE REGULARITY OFPHI-HARMONIC MAPS

摘要

We extend the p-harmonic approximation lemma proved by Duzaar andMingione for p-harmonic functions to phi-harmonic functions, where phi is a convex function.The proof is direct and is based on the Lipschitz truncation technique. We applythe approximation lemma to prove Holder continuity for the gradient of a solution of aphi-harmonic system with critical growth.