R^(n)中单位球上满足Poisson方程的边界Schwarz引理  

Boundary Schwarz Lemma of the Unit Ball in R^(n)Satisfying Poisson's Equation

作　　者：陈铭新 王建飞 唐笑敏[2] Ming Xin CHEN;Jian Fei WANG;Xiao Min TANG(School of Mathematical Sciences,Huaqiao University,Quanzhou 362021,P.R.China;Department of Mathematics,Huzhou Teachers College,Huzhou 313000,P.R.China)

机构地区：[1]华侨大学数学科学学院,泉州362021 [2]湖州师范学院理学院,湖州313000

出　　处：《数学学报（中文版）》2023年第4期717-726,共10页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(12071161,12071130,11971165);福建省自然科学基金(2020J01073,2019J01066)。

摘　　要：Schwarz引理在全纯映射和调和映射理论中扮演着重要的角色.本文建立了R^(n)中单位球上满足Poisson方程解的边界Schwarz引理.作为应用,给出了单位球上调和自映射的边界Schwarz引理,将平面上的多重调映射结果和边界Schwarz引理推广到了高维调和映射.Schwarz lemma plays significant roles on function theory of holomorphic mappings or harmonic mappings.In this paper,we establish the Schwarz lemma at the boundary for self-mappings solutions satisfying the Poisson's equation of the unit ball in R^(n).As an application,the boundary Schwarz lemma for harmonic self-mappings on the unit ball is obtained which extends the result of pluriharmonic mappings to harmonic mappings in higher dimensions.

关 键 词：调和映射 边界Schwarz引理 POISSON方程 

分 类 号：O174.5[理学—数学]