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Harmonic Green and Neumann functions for domains bounded by two intersecting circular arcs
Complex Variables and Elliptic Equations ( IF 0.9 ) Pub Date : 2020-09-20 , DOI: 10.1080/17476933.2020.1816984
Hanxing Lin 1
Affiliation  

ABSTRACT

The parqueting-reflection principle is shown to work for constructing the harmonic Green functions and harmonic Neumann functions for a class of domains, which are bounded by two intersecting circular arcs in C with a particular angle π/n,nN. With the explicit expressions of the harmonic Green and Neumann functions, we solve the Dirichlet and Neumann boundary problems to the Poisson equation in these domains by applying the Green and Neumann representation formulas.



中文翻译:

由两个相交圆弧界定的域的调和格林函数和诺伊曼函数

摘要

parqueting-reflection 原理被证明适用于为一类域构造调和格林函数和调和诺伊曼函数,这些域由两个相交的圆弧在C以特定的角度π/n,nñ*. 通过调和格林函数和诺伊曼函数的显式表达式,我们通过应用格林和诺伊曼表示公式解决了这些域中泊松方程的狄利克雷和诺伊曼边界问题。

更新日期:2020-09-20
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