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

[31] Representation of the Green's Function of the Dirichlet Problem for the Polyharmonic Equation in the Ball
Karachik, V. V.
DIFFERENTIAL EQUATIONS, 2023, 59 (08) : 1061 - 1074
[32] On solutions of the mixed Dirichlet–Navier problem for the polyharmonic equation in exterior domains
O. A. Matevosyan
Russian Journal of Mathematical Physics, 2016, 23 : 135 - 138
[33] On a new method for constructing the Green function of the Dirichlet problem for the polyharmonic equation
Kal'menov, T. Sh.
Suragan, D.
DIFFERENTIAL EQUATIONS, 2012, 48 (03) : 441 - 445
[34] On a new method for constructing the Green function of the Dirichlet problem for the polyharmonic equation
T. Sh. Kal’menov
D. Suragan
Differential Equations, 2012, 48 : 441 - 445
[35] Representation for the Green's function of the Dirichlet problem for polyharmonic equations in a ball
Kal'menov, T. Sh.
Koshanov, B. D.
SIBERIAN MATHEMATICAL JOURNAL, 2008, 49 (03) : 423 - 428
[36] Representation of the Green’s Function of the Dirichlet Problem for the Polyharmonic Equation in the Ball
V. V. Karachik
Differential Equations, 2023, 59 : 1061 - 1074
[37] Representation for the Green’s function of the Dirichlet problem for polyharmonic equations in a ball
T. Sh. Kal’menov
B. D. Koshanov
Siberian Mathematical Journal, 2008, 49 : 423 - 428
[38] The Dirichlet problem for polyanalytic functions
Mazalov, M. Ya.
SBORNIK MATHEMATICS, 2009, 200 (9-10) : 1473 - 1493
[39] The fundamental functions and the Dirichlet problem
Stekloff, W
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES, 1900, 131 : 870 - 873
[40] ANALYTIC FUNCTIONS + DIRICHLET PROBLEM
LUMER, G
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1964, 70 (01) : 98 - &

← 1 2 3 4 5 →