与双调和方程相关的连续模和Heinz-Schwarz型不等式

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与双调和方程相关的连续模和Heinz-Schwarz型不等式陈少林衡阳师范学院数学与统计学院衡阳 421008 Modulus of Continuity and Heinz-Schwarz Type Inequalities of Solutions to Biharmonic Equations Shao Lin CHENCollege of Mathematics and Statistics, Hengyang Normal University, Hengyang 421008, P. R. China

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摘要对于给定的两个正整数n ≥ 2和m ≥ 1，假设函数f满足如下条件：（1）在Bⁿ内满足非齐次双调和方程△（△f）=g（g ∈ C（Bⁿ，R^m））；（2）在S^n-1上满足f=ψ₁（ψ₁ ∈ C（S^n-1，R^m）），以及∂f/∂n=ψ₂（ψ₂ ∈ C（S^n-1，R^m）），其中∂/∂n表示内法线方向导数，Bⁿ表示Rⁿ中的单位球以及S^n-1表示Bⁿ的边界.本文主要研究f的连续模和Heinz-Schwarz型不等式.

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收稿日期: 2019-09-19

MR (2010):

O177.2

基金资助:湖南省教育厅优秀青年基金项目（18B365）；湖南省科技计划项目（2016TP1020）；湖南省高等学校双一流应用特色学科"数学"（湘教通[2018]469）；衡阳市科技计划项目（2018KJ125）

作者简介: 陈少林,E-mail:mathechen@126.com

引用本文:

陈少林. 与双调和方程相关的连续模和Heinz-Schwarz型不等式[J]. 数学学报, 2020, 63(5): 505-522. Shao Lin CHEN. Modulus of Continuity and Heinz-Schwarz Type Inequalities of Solutions to Biharmonic Equations. Acta Mathematica Sinica, Chinese Series, 2020, 63(5): 505-522.

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