数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (2): 633-645.doi: 10.1007/s10473-021-0221-2

• 论文 • 上一篇    下一篇

REGULARITY OF P-HARMONIC MAPPINGS INTO NPC SPACES

郭常予1, 向长林2   

  1. 1. Research Center for Mathematics and Interdisciplinary Sciences, Shandong University, Qingdao 266237, China;
    2. School of Information and Mathematics, Yangtze University, Jingzhou 434023, China
  • 收稿日期:2020-03-26 修回日期:2020-06-26 出版日期:2021-04-25 发布日期:2021-04-29
  • 通讯作者: Changlin XIANG E-mail:changlin.xiang@yangtzeu.edu.cn
  • 作者简介:Changyu GUO,E-mail:changyu.guo@email.sdu.edu.cn
  • 基金资助:
    C.Y. Guo is supported by the Qilu funding of Shandong University (62550089963197); C.L. Xiang is financially supported by the National Natural Science Foundation of China (11701045) and the Yangtze Youth Fund (2016cqn56).

REGULARITY OF P-HARMONIC MAPPINGS INTO NPC SPACES

Changyu GUO1, Changlin XIANG2   

  1. 1. Research Center for Mathematics and Interdisciplinary Sciences, Shandong University, Qingdao 266237, China;
    2. School of Information and Mathematics, Yangtze University, Jingzhou 434023, China
  • Received:2020-03-26 Revised:2020-06-26 Online:2021-04-25 Published:2021-04-29
  • Contact: Changlin XIANG E-mail:changlin.xiang@yangtzeu.edu.cn
  • About author:Changyu GUO,E-mail:changyu.guo@email.sdu.edu.cn
  • Supported by:
    C.Y. Guo is supported by the Qilu funding of Shandong University (62550089963197); C.L. Xiang is financially supported by the National Natural Science Foundation of China (11701045) and the Yangtze Youth Fund (2016cqn56).

摘要: 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 $u\colon M\to X$ 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 ($p\geq 2$) associated to our notion of $p$-energy is locally H\"older continuous whenever its image lies in a compact subset of $X$.

关键词: Alexandrov space with non-positive curvature, p-harmonic mappings, upper gradients, Korevaar-Schoen Sobolev space

Abstract: 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 $u\colon M\to X$ 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 ($p\geq 2$) associated to our notion of $p$-energy is locally H\"older continuous whenever its image lies in a compact subset of $X$.

Key words: Alexandrov space with non-positive curvature, p-harmonic mappings, upper gradients, Korevaar-Schoen Sobolev space

中图分类号: 

  • 58E15