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

We extend the p-harmonic approximation lemma proved by Duzaar and Mingione 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 apply the approximation lemma to prove Wilder continuity for the gradient of a solution of a phi-harmonic system with critical growth. (c) 2012 Elsevier Inc. All rights reserved.