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.

引用

页码：435 / 457

页数：23

共 50 条

[21] Dirichlet problem for a generalized inhomogeneous polyharmonic equation in an annular domain
Aksoy, U.
Celebi, A. O.
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2012, 57 (2-4) : 229 - 241
[22] A dirichlet problem for the inhomogeneous polyharmonic equation in the upper half plane
Begehr, Heinrich
Gaertner, Evgenija
GEORGIAN MATHEMATICAL JOURNAL, 2007, 14 (01) : 33 - 52
[23] On Green's Function of the Dirichlet Problem for the Polyharmonic Equation in the Ball
Karachik, Valery
AXIOMS, 2023, 12 (06)
[24] Green function representation for the Dirichlet problem of the polyharmonic equation in a sphere
Kalmenov, T. Sh.
Koshanov, B. D.
Nemchenko, M. Y.
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2008, 53 (02) : 177 - 183
[25] Solution of the Dirichlet problem with polynomial data for the polyharmonic equation in a ball
V. V. Karachik
Differential Equations, 2015, 51 : 1033 - 1042
[26] On the representation of the Green function of the Dirichlet problem and their properties for the polyharmonic equations
Koshanov, Bakytbek D.
Koshanova, Maira D.
ADVANCEMENTS IN MATHEMATICAL SCIENCES (AMS 2015), 2015, 1676
[27] Construction of polynomial solutions to the Dirichlet problem for the polyharmonic equation in a ball
V. V. Karachik
Computational Mathematics and Mathematical Physics, 2014, 54 : 1122 - 1143
[28] Green function representation in the Dirichlet problem for polyharmonic equations in a ball
Kal'menov, T. Sh.
Koshanov, B. D.
Nemchenko, M. Yu.
DOKLADY MATHEMATICS, 2008, 78 (01) : 528 - 530
[29] Construction of polynomial solutions to the Dirichlet problem for the polyharmonic equation in a ball
Karachik, V. V.
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2014, 54 (07) : 1122 - 1143
[30] Polyharmonic dirichlet problems
H. Begehr
T. N. H. Vu
Z. -X. Zhang
Proceedings of the Steklov Institute of Mathematics, 2006, 255 (1) : 13 - 34

← 1 2 3 4 5 →