一族非齐次双调和方程解的边界Schwarz引理

数学物理学报 ›› 2022, Vol. 42 ›› Issue (6): 1633-1639.

一族非齐次双调和方程解的边界Schwarz引理

白晓瑾^1,²(),朱剑峰^2,*()

¹ 武汉大学数学与统计学院武汉 430072
² 华侨大学数学科学学院福建泉州 362021

收稿日期:2020-05-14 出版日期:2022-12-26 发布日期:2022-12-16
通讯作者: 朱剑峰 E-mail:xiaojin_bai@foxmail.com;flandy@hqu.edu.cn
作者简介:白晓瑾, E-mail: xiaojin_bai@foxmail.com
基金资助:
国家自然科学基金(12271189);国家自然科学基金(11971182);福建省面上基金(2021J01304);福建省面上基金(2019J0101)

Boundary Schwarz Lemma for Solutions to a Class of Inhomogeneous Biharmonic Equations

Xiaojin Bai^1,²(),Jianfeng Zhu^2,*()

¹ School of Mathematics and Statistics, Wuhan University, Wuhan 430072
² School of Mathematical Sciences, Huaqiao University, Fujian Quanzhou 362021

Received:2020-05-14 Online:2022-12-26 Published:2022-12-16
Contact: Jianfeng Zhu E-mail:xiaojin_bai@foxmail.com;flandy@hqu.edu.cn
Supported by:
the NSFC(12271189);the NSFC(11971182);the NSF of Fujian Province(2021J01304);the NSF of Fujian Province(2019J0101)

摘要/Abstract

摘要：

令$\mathbb{D}$为单位圆, ${\mathbb{T}}$为单位圆周.设$f$是满足边界条件: $(\Delta f)|_{{\mathbb{T}}}=\psi$和$f|_{{\mathbb{T}}}=f^*$的非齐次双调和方程$\Delta(\Delta f)=g$的解, 其中$g\in{\cal C}(\overline{\mathbb{D}})$, 而$\psi$和$f^*$皆为${\mathbb{T}}$上的连续函数.该文建立了该族解$f$的边界Schwarz引理, 这一结果丰富了边界Schwarz引理在平面上的相关结果.

关键词: 非齐次双调和方程, 解, Dirichlet问题, 边界Schwarz引理

Abstract:

Let $\mathbb{D}$ be the unit disk, ${\mathbb T}$ the unit circle. Assume that $f$ is a solution to inhomogeneous biharmonic equation: $\Delta f=g$, satisfying the boundary conditions: $(\Delta f)_{{\mathbb T}}=\psi$ and $f|_{{\mathbb T}}=f^*$, where $g\in {\cal C}(\overline{\mathbb{D}})$, and $\psi, f^*\in {\cal C}({\mathbb T})$ are continuous functions. In this paper, we establish the boundary Schwarz lemma for solutions $f$, this result enriches the related results of boundary Schwarz lemma on the plane.

Key words: Inhomogeneous biharmonic equations, Solution, Dirichlet problem, Boundary Schwarz lemma

中图分类号:

O174.2

白晓瑾,朱剑峰. 一族非齐次双调和方程解的边界Schwarz引理[J]. 数学物理学报, 2022, 42(6): 1633-1639.

Xiaojin Bai,Jianfeng Zhu. Boundary Schwarz Lemma for Solutions to a Class of Inhomogeneous Biharmonic Equations[J]. Acta mathematica scientia,Series A, 2022, 42(6): 1633-1639.

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