IMPROVED REGULARITY OF HARMONIC DIFFEOMORPHIC EXTENSIONS ON QUASIHYPERBOLIC DOMAINS

被引：0

作者：

Wang, Zhuang ^{[1
]}

Xu, Haiqing ^{[2
]}

机构：

[1] Hunan Normal Univ, Sch Math & Stat, MOE LCSM, Changsha 410081, Peoples R China

[2] Shandong Univ, Frontiers Sci Ctr Nonlinear Expectat, Res Ctr Math & Interdisciplinary Sci, Minist Educ China, Qingdao 266237, Peoples R China

来源：

ACTA MATHEMATICA SCIENTIA | 2023年 / 43卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Poisson extension; Orlicz-Sobolev homeomorphisms; weighted Sobolev homeomorphisms; quasihyperbolic domains; BOUNDARY-CONDITIONS; HOLDER CONTINUITY; MAPPINGS; CAPACITY;

D O I：

10.1007/s10473-023-0121-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let X be a Jordan domain satisfying certain hyperbolic growth conditions. Assume that phi is a homeomorphism from the boundary partial derivative X of X onto the unit circle. Denote by h the harmonic diffeomorphic extension of phi from 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].

引用

页码：373 / 386

页数：14

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