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
收藏
页码：423 / 428
页数：6
相关论文
共 50 条
  • [41] Riquier–Neumann Problem for the Polyharmonic Equation in a Ball
    V. V. Karachik
    Differential Equations, 2018, 54 : 648 - 657
  • [42] Green's Function for the Dirichlet Boundary Value Problem in a Domain with Several Inclusions
    Maz'ya, V.
    Movchan, A.
    Nieves, M.
    GREEN'S KERNELS AND MESO-SCALE APPROXIMATIONS IN PERFORATED DOMAINS, 2013, 2077 : 59 - 73
  • [43] On Green’s function of Cauchy–Dirichlet problem for hyperbolic equation in a quarter plane
    Makhmud Sadybekov
    Bauyrzhan Derbissaly
    Boundary Value Problems, 2021
  • [44] On solvability of polyharmonic Dirichlet problem in symmetric Sobolev spaces
    Bilalov, Bilal T.
    Sadigova, Sabina R.
    Sezer, Yonca
    Nasibova, Natavan P.
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2024, 47 (18) : 14386 - 14401
  • [45] THE DIRICHLET PROBLEM FOR THE POLYHARMONIC EQUATION IN LIPSCHITZ-DOMAINS
    VERCHOTA, G
    INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1990, 39 (03) : 671 - 702
  • [46] Dirichlet and Neumann Boundary Value Problems for the Polyharmonic Equation in the Unit Ball
    Karachik, Valery
    MATHEMATICS, 2021, 9 (16)
  • [47] Lp polyharmonic Dirichlet problems in regular domains III: The unit ball
    Du, Zhihua
    Qian, Tao
    Wang, Jinxun
    COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2014, 59 (07) : 947 - 965
  • [48] On solutions of the Dirichlet problem for the polyharmonic equation in unbounded domains
    Matevossian H.A.
    P-Adic Numbers, Ultrametric Analysis, and Applications, 2015, 7 (1) : 71 - 75
  • [49] Garabedian's Way for the Polyharmonic Green-Almansi Function
    Begehr, Heinrich
    Gilbert, Robert P.
    Xu, Steve Yongzhi
    LOBACHEVSKII JOURNAL OF MATHEMATICS, 2024, 45 (08) : 3504 - 3508
  • [50] Representation of the Green’s function of the exterior Neumann problem for the Laplace operator
    M. A. Sadybekov
    B. T. Torebek
    B. Kh. Turmetov
    Siberian Mathematical Journal, 2017, 58 : 153 - 158
12345