Schwarz boundary value problem for the Cauchy-Riemann equation in a rectangle

Boundary value problems

Xuefang Zhao¹  Ying Wang² 

[1] College of Mathematics and Econometrics, Hunan University, Changsha, P.R. China;School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, P.R. China

关键词: Schwarz-Poisson formula;    Cauchy-Riemann equation;    Schwarz problem;    30E25;    35C15;    35F45;   

DOI  :  10.1186/s13661-016-0520-z

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, Schwarz problem for the inhomogeneous Cauchy-Riemann equation in a rectangle is investigated explicitly. By the parqueting reflection principle and the Cauchy-Pompeiu formula, a modified Schwarz-Poisson representation formula in a rectangle is constructed. In particular, the boundary behaviors for the related Schwarz-type and Pompeiu-type operators at the corner points are discussed in detail.

【 授权许可】

CC BY