Representation for the Green's function of the Dirichlet problem for polyharmonic equations in a ball

被引：28

作者：

Kal'menov, T. Sh. ^{[1
]}

Koshanov, B. D. ^{[1
]}

机构：

[1] Minist Educ & Sci Republ Kazakhstan, Res Ctr Phys & Math, Alma Ata, Kazakhstan

来源：

SIBERIAN MATHEMATICAL JOURNAL | 2008年 / 49卷 / 03期

关键词：

polyharmonic equation; Dirichlet problem; Green's function;

D O I：

10.1007/s11202-008-0042-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We explicitly construct the Green's function for the Dirichlet problem for polyharmonic equations in a ball in a space of arbitrary dimension. The formulas for the Green's function are of interest in their own right. In particular, the explicit representations for a solution to the Dirichlet problem for the biharmonic equation are important in elasticity.

引用

页码：423 / 428

页数：6

共 50 条

[31] On solutions of the Dirichlet problem for the polyharmonic equation in unbounded domains [J].

Matevossian H.A. .

P-Adic Numbers, Ultrametric Analysis, and Applications, 2015, 7 (1) :71-75

[32] Representation of the Green's function of the exterior Neumann problem for the Laplace operator [J].

Sadybekov, M. A. ;

Torebek, B. T. ;

Turmetov, B. Kh. .

SIBERIAN MATHEMATICAL JOURNAL, 2017, 58 (01) :153-158

[33] On solution uniqueness of the Dirichlet problem for a system of partial differential equations on one function in the unit ball [J].

Beloglyadov, Michail V. ;

Burskii, Vladimir P. .

JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 2011, 19 (01) :13-23

[34] Dirichlet problem for a generalized inhomogeneous polyharmonic equation in an annular domain [J].

Aksoy, U. ;

Celebi, A. O. .

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2012, 57 (2-4) :229-241

[35] A dirichlet problem for the inhomogeneous polyharmonic equation in the upper half plane [J].

Begehr, Heinrich ;

Gaertner, Evgenija .

GEORGIAN MATHEMATICAL JOURNAL, 2007, 14 (01) :33-52

[36] A Dirichlet type problem for complex polyharmonic functions [J].

Grzebula, H. ;

Michalik, S. .

ACTA MATHEMATICA HUNGARICA, 2017, 153 (01) :216-229

[37] A Dirichlet type problem for complex polyharmonic functions [J].

H. Grzebuła ;

S. Michalik .

Acta Mathematica Hungarica, 2017, 153 :216-229

[38] Representation of the Green’s function of the exterior Neumann problem for the Laplace operator [J].

M. A. Sadybekov ;

B. T. Torebek ;

B. Kh. Turmetov .

Siberian Mathematical Journal, 2017, 58 :153-158

[39] Dirichlet and Neumann Boundary Value Problems for Dunkl Polyharmonic Equations [J].

Yuan, Hongfen ;

Karachik, Valery .

MATHEMATICS, 2023, 11 (09)

[40] On Stochastic Representation for Solutions of the Dirichlet Problem for Elliptic Equations in Divergence Form [J].

Rozkosz, Andrzej .

STOCHASTIC ANALYSIS AND APPLICATIONS, 2009, 27 (01) :1-15

← 1 2 3 4 5 →