• 论文 •

### 一族非齐次双调和方程解的边界Schwarz引理

1. 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 Bai1,2(),Jianfeng Zhu2,*()

1. 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)

$\mathbb{D}$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$$f|_{{\mathbb{T}}}=f^*的非齐次双调和方程\Delta(\Delta f)=g的解, 其中g\in{\cal C}(\overline{\mathbb{D}}), 而\psi$$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.

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.

• O174.2