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

[21] GREEN FUNCTION FOR ANALOGUE OF ROBIN PROBLEM FOR POLYHARMONIC EQUATION [J].

Turmetov, B. Kh .

UFA MATHEMATICAL JOURNAL, 2019, 11 (03) :78-87

[22] Dirichlet problem for inhomogeneous polyharmonic equation [J].

Kumar, Ajay ;

Prakash, Ravi .

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2008, 53 (07) :643-651

[23] Dirichlet and Neumann Boundary Value Problems for the Polyharmonic Equation in the Unit Ball [J].

Karachik, Valery .

MATHEMATICS, 2021, 9 (16)

[24] Green's function of one problem for the 3-harmonic equation in a ball [J].

Karachik, V. V. .

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2025,

[25] A Dirichlet problem for polyharmonic functions [J].

Begehr, Heinrich ;

Du, Jinyuan ;

Wang, Yufeng .

ANNALI DI MATEMATICA PURA ED APPLICATA, 2008, 187 (03) :435-457

[26] A Dirichlet problem for polyharmonic functions [J].

Heinrich Begehr ;

Jinyuan Du ;

Yufeng Wang .

Annali di Matematica Pura ed Applicata, 2008, 187 :435-457

[27] Riquier-Neumann Problem for the Polyharmonic Equation in a Ball [J].

Karachik, Valery .

MATHEMATICS, 2023, 11 (04)

[28] Solvability of the Neumann Boundary Value Problem for the Polyharmonic Equation in a Ball [J].

Karachik, V. .

LOBACHEVSKII JOURNAL OF MATHEMATICS, 2024, 45 (08) :3559-3571

[29] CONSTRUCTION OF GREEN'S FUNCTION OF THE NEUMANN PROBLEM IN A BALL [J].

Sadybekov, M. A. ;

Torebek, B. T. ;

Turmetov, B. Kh. .

EURASIAN MATHEMATICAL JOURNAL, 2016, 7 (02) :100-105

[30] On solvability of polyharmonic Dirichlet problem in symmetric Sobolev spaces [J].

Bilalov, Bilal T. ;

Sadigova, Sabina R. ;

Sezer, Yonca ;

Nasibova, Natavan P. .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2024, 47 (18) :14386-14401

← 1 2 3 4 5 →