| 保角映射与格林函数 |
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| 引用本文： | 刘德朋. 保角映射与格林函数[J]. 浙江师范大学学报(自然科学版), 2001, 24(3): 257-259 |
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| 作者姓名： | 刘德朋 |
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| 作者单位： | 四平师范学院数学系, |
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| 摘 要： | 旨在利用数学物理方程解的积分公式，去解决平面角形区域内Laplace方程和Poisson方程的边值问题，而其关键在于构造相应域内的格林函数，这里以上半平面内的像点为基础，通过保角映射将角形区域映射到上半平面后，找出相应域内的像点，推出其格林函数，使问题得到解决，并将此结果推广到三维空间的角状区域上。
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| 关 键 词： | 保角映射 像点 格林函数 数学物理方程 Laplace方程 Poisson方程 |
| 文章编号： | 1001-5051-(2001)03-0257-03 |
| 修稿时间： | 2000-11-05 |
Angle-preserving mapping and Green function |
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| LIU De-peng. Angle-preserving mapping and Green function[J]. Journal of Zhejiang Normal University Natural Sciences, 2001, 24(3): 257-259 |
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| Authors: | LIU De-peng |
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| Abstract: | The paper aimed at resolving the question of side value of Laplace equation and Poisson equation in plane angular domain by using integral equation of the solution of mathematic physics equation.The key problem was to construct the Green function in the corresponding domain.It based on the image points in the upper semi-plane,the angular domain was mapped into upper semi-plane via angle-preserving mapping,then found out the image points in the corresponding domain,finally Green function in angular domain was obtained.The result could be extended into the angular domain in three dimensions. |
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