REGULARITY OF P-HARMONIC MAPPINGS INTO NPC SPACES

Let M be a C^(2)-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.