The φ-harmonic approximation and the regularity of φ-harmonic maps

Abstract

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