IMPROVED REGULARITY OF HARMONIC DIFFEOMORPHIC EXTENSIONS ON QUASIHYPERBOLIC DOMAINS*

doi:10.1007/s10473-023-0121-8

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (1): 373-386.doi: 10.1007/s10473-023-0121-8

IMPROVED REGULARITY OF HARMONIC DIFFEOMORPHIC EXTENSIONS ON QUASIHYPERBOLIC DOMAINS^*

Zhuang Wang¹, Haiqing Xu^2,†

1. MOE-LCSM, School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China;
2. Frontiers Science Center for Nonlinear Expectations (Ministry of Education of China), Research Center for Mathematics and Interdisciplinary Sciences, Shandong University, Qingdao 266237, China

收稿日期:2021-04-25 修回日期:2022-06-14 发布日期:2023-03-01
通讯作者: †Haiqing XU. E-mail: hqxu@mail.ustc.edu.cn
基金资助:
*Young Scientist Program of the Ministry of Science and Technology of China (2021YFA1002200). The first author was supported by National Natural Science Foundation of China (12101226). The second author was supported by Shandong Provincial Natural Science Foundation (ZR2021QA032), and partially supported by the National Natural Science Foundation of China (12101362).

IMPROVED REGULARITY OF HARMONIC DIFFEOMORPHIC EXTENSIONS ON QUASIHYPERBOLIC DOMAINS^*

Zhuang Wang¹, Haiqing Xu^2,†

1. MOE-LCSM, School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China;
2. Frontiers Science Center for Nonlinear Expectations (Ministry of Education of China), Research Center for Mathematics and Interdisciplinary Sciences, Shandong University, Qingdao 266237, China

Received:2021-04-25 Revised:2022-06-14 Published:2023-03-01
Contact: †Haiqing XU. E-mail: hqxu@mail.ustc.edu.cn
About author:Zhuang Wang,E-mail: zwang@hunnu.edu.cn
Supported by:
*Young Scientist Program of the Ministry of Science and Technology of China (2021YFA1002200). The first author was supported by National Natural Science Foundation of China (12101226). The second author was supported by Shandong Provincial Natural Science Foundation (ZR2021QA032), and partially supported by the National Natural Science Foundation of China (12101362).

摘要/Abstract

摘要： Let $\mathbb{X}$ be a Jordan domain satisfying certain hyperbolic growth conditions. Assume that $\varphi$ is a homeomorphism from the boundary $\partial \mathbb{X}$ of $\mathbb{X}$ onto the unit circle. Denote by $h$ the harmonic diffeomorphic extension of $\varphi $ from $\mathbb{X}$ onto the unit disk. We establish the optimal Orlicz-Sobolev regularity and weighted Sobolev estimate of $h.$ These generalize the Sobolev regularity of $h$ in [A. Koski, J. Onninen, Sobolev homeomorphic extensions, J. Eur. Math. Soc. 23 (2021) 4065-4089, Theorem 3.1].

关键词: Poisson extension, Orlicz-Sobolev homeomorphisms, weighted Sobolev homeomorphisms, quasihyperbolic domains

Abstract: Let $\mathbb{X}$ be a Jordan domain satisfying certain hyperbolic growth conditions. Assume that $\varphi$ is a homeomorphism from the boundary $\partial \mathbb{X}$ of $\mathbb{X}$ onto the unit circle. Denote by $h$ the harmonic diffeomorphic extension of $\varphi $ from $\mathbb{X}$ onto the unit disk. We establish the optimal Orlicz-Sobolev regularity and weighted Sobolev estimate of $h.$ These generalize the Sobolev regularity of $h$ in [A. Koski, J. Onninen, Sobolev homeomorphic extensions, J. Eur. Math. Soc. 23 (2021) 4065-4089, Theorem 3.1].

Key words: Poisson extension, Orlicz-Sobolev homeomorphisms, weighted Sobolev homeomorphisms, quasihyperbolic domains

Zhuang Wang, Haiqing Xu. IMPROVED REGULARITY OF HARMONIC DIFFEOMORPHIC EXTENSIONS ON QUASIHYPERBOLIC DOMAINS^*[J]. 数学物理学报(英文版), 2023, 43(1): 373-386.

Zhuang Wang, Haiqing Xu. IMPROVED REGULARITY OF HARMONIC DIFFEOMORPHIC EXTENSIONS ON QUASIHYPERBOLIC DOMAINS^*[J]. Acta mathematica scientia,Series B, 2023, 43(1): 373-386.

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IMPROVED REGULARITY OF HARMONIC DIFFEOMORPHIC EXTENSIONS ON QUASIHYPERBOLIC DOMAINS^*

IMPROVED REGULARITY OF HARMONIC DIFFEOMORPHIC EXTENSIONS ON QUASIHYPERBOLIC DOMAINS^*

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