A Dirichlet problem for polyharmonic functions

被引：56
|
作者：
Begehr, Heinrich [1 ]
Du, Jinyuan [2 ]
Wang, Yufeng [2 ]
机构：
[1] Free Univ Berlin, Inst Math 1, D-14159 Berlin, Germany
[2] Wuhan Univ, Dept Math, Wuhan 430072, Peoples R China
来源：
ANNALI DI MATEMATICA PURA ED APPLICATA | 2008年 / 187卷 / 03期
基金：
中国国家自然科学基金;
关键词：
polyharmonic function; polyanalytic function; analytic function; Kernel function; Dirichlet problem; Riemann boundary value problem;
D O I：
10.1007/s10231-007-0050-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, the Dirichlet problem of polyharmonic functions is considered. As well the explicit expression of the unique solution to the simple Dirichlet problem for polyharmonic functions is obtained by using the decomposition of polyharmonic functions and turning the problem into an equivalent Riemann boundary value problem for polyanalytic functions, as the approach to find the kernel functions of the solution for the general Dirichlet problem is given.
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页码：435 / 457
页数：23
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