REGULARITY OF P-HARMONIC MAPPINGS INTO NPC SPACES

doi:10.1007/s10473-021-0221-2

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

REGULARITY OF P-HARMONIC MAPPINGS INTO NPC SPACES

郭常予¹, 向长林²

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. 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/Abstract

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

郭常予, 向长林. REGULARITY OF P-HARMONIC MAPPINGS INTO NPC SPACES[J]. 数学物理学报(英文版), 2021, 41(2): 633-645.

Changyu GUO, Changlin XIANG. REGULARITY OF P-HARMONIC MAPPINGS INTO NPC SPACES[J]. Acta mathematica scientia,Series B, 2021, 41(2): 633-645.

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REGULARITY OF P-HARMONIC MAPPINGS INTO NPC SPACES

REGULARITY OF P-HARMONIC MAPPINGS INTO NPC SPACES

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