REGULARITY OF P-HARMONIC MAPPINGS INTO NPC SPACES

• 来源期刊: 数学物理学报（英文版）
• 年，卷（期）: 2021,（2）
• 页码范围: 633-645
• 页数: 13页
• 语种: 英文
• DOI: 10.3969/j.issn.0252-9602.2021.02.021

摘要

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 H(o)lder continuous whenever its image lies in a compact subset of X.