论文标题
Schwarz边界值问题的多序分析方程
Schwarz boundary value problems for polyanalytic equation in a sector ring
论文作者
论文摘要
在本文中，我们首先通过适当的共形映射给出了整个部门环中修改的Schwarz-Pompeiu公式，并以显式形式获得了Cauchy-Riemann方程的Schwarz问题解决方案。此外，引入了一类积分运算符及其属性。最后，分别研究了针对不均匀的多架方程和广义多芯片方程的施瓦茨问题。
In this article,we first give a modified Schwarz-Pompeiu formula in a general sector ring by proper conformal mappings, and obtain the solution of the Schwarz problem for the Cauchy-Riemann equation in explicit forms. Furthermore, a class of integral operators is introduced together with their properties. Finally, by virtue of these operators, Schwarz problems for a inhomogeneous polyanalytic equation and for a generalized polyanalytic equation are investigated, respectively.
