IMPROVED REGULARITY OF HARMONIC DIFFEOMORPHIC EXTENSIONS ON QUASIHYPERBOLIC DOMAINS  

作　　者：王壮 徐海清 Zhuang WANG;Haiqing XU(MOE-LCSM,School of Mathematics and Statistics,Hunan Normal University,Changsha,410081,China;Frontiers Science Center for Nonlinear Expectations(Ministry of Education of China),Research Center for Mathematics and Interdisciplinary Sciences,Shandong University,Qingdao,266237,China)

机构地区：[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

出　　处：《Acta Mathematica Scientia》2023年第1期373-386,共14页数学物理学报（B辑英文版）

基　　金：partially supported by the Young Scientist Program of the Ministry of Science and Technology of China(2021YFA1002200);supported by National Natural Science Foundation of China(12101226);partially supported by the National Natural Science Foundation of China(12101362);supported by Shandong Provincial Natural Science Foundation(ZR2021QA032)。

摘　　要：Let X be a Jordan domain satisfying certain hyperbolic growth conditions.Assume that φ is a homeomorphism from the boundary ?X of X onto the unit circle.Denote by h the harmonic diffeomorphic extension of φ 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].

关 键 词：Poisson extension Orlicz-Sobolev homeomorphisms weighted Sobolev homeomorphisms quasihyperbolic domains 

分 类 号：O175[理学—数学]