Some regularity results for p-harmonic mappings between Riemannian manifolds. (November 2019)

• Record Type: Journal Article
• Authors: Guo, Chang-Yu; Xiang, Chang-Lin
• Is Part Of: Nonlinear analysis. Volume 188(2019)
• Page Start: 405
• Page End: 424
• Publication Date: 2019-11
• Subjects: 58E20; Non-positive curvature -- Regular geodesic ball -- p-harmonic mappings -- Interior regularity -- Gradient estimate -- Liouville theorem; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.06.006
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: 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, α for some α ∈ ( 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.