Regularity of P-Harmonic Mappings into NPC Spaces

Abstract

Let M be a C2-smooth Riemannian manifold with boundary and X be a metric space with non-positive curvature in the sense of Alexandrov. Let u: M → X be a Sobolev mapping in the sense of Korevaar and Schoen. In this short note, we introduce a notion of p-energy for u which is slightly different from the original definition of Korevaar and Schoen. We show that each minimizing p-harmonic mapping (p ≥ 2) associated to our notion of p-energy is locally Holder continuous whenever its image lies in a compact subset of X.