Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (6): 1633-1639.

Previous Articles     Next Articles

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;
  • Supported by:
    the NSFC(12271189);the NSFC(11971182);the NSF of Fujian Province(2021J01304);the NSF of Fujian Province(2019J0101)


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

CLC Number: 

  • O174.2