Some regularity results for p-harmonic mappings between Riemannian manifolds

Let M be a C-2-smooth Riemannian manifold with boundary and N a complete C-2-smooth Riemannian manifold. We show that each stationary p-harmonic mapping u: M -> N, whose image lies in a compact subset of N, is locally C-1,C-alpha for some alpha is an element of (0, 1), provided that N is simply connected and has non-positive sectional curvature. We also prove similar results for minimizing p-harmonic mappings with image being contained in a regular geodesic ball. Moreover, when M has non-negative Ricci curvature and N is simply connected with non-positive sectional curvature, we deduce a gradient estimate for C-1-smooth weakly p-harmonic mappings from which follows a Liouville-type theorem in the same setting. (C) 2019 Elsevier Ltd. All rights reserved.