Solution to the Dirichlet Problem for the Polyharmonic Equation in the Ball

被引：0
作者：
Karachik V.V. [1 ]
机构：
[1] South Ural State University, Chelyabinsk
来源：
Siberian Advances in Mathematics | 2022年 / 32卷 / 3期
关键词：
Almansi representation; Dirichlet problem; Green’s function; polyharmonic equation;
D O I：
10.1134/S1055134422030038
中图分类号：
学科分类号：
摘要：
Abstract: We give a representation of the solution to the Dirichlet problem for the inhomogeneouspolyharmonic equation in the unit ball in terms of solutions to the Dirichlet problem for theLaplace equation. © 2022, Pleiades Publishing, Ltd.
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页码：197 / 210
页数：13
相关论文
共 21 条
[1]  
Alimov S.A., A problem involving an inclined derivative, Differ. Equ., 17, (1982)
[2]  
Almansi E., Sull’integrazione dell’equazione differenziale u = 0, Ann. Mat. Pura Appl., 2, 3, (1899)
[3]  
Begehr H., Biharmonic Green functions, Le Matematiche, pp. 395-405, (2006)
[4]  
Begehr H., Vu T.N.H., Zhang Z.-X., Polyharmonic Dirichlet Problems, Proc. Steklov Inst. Math., 255, (2006)
[5]  
Bitsadze A.V., Equations of Mathematical Physics, (1982)
[6]  
Boggio T., Sulle funzioni di Green d’ordine m, Rend. Circ. Mat. Palermo., 20, (1905)
[7]  
Erdelyi A., Magnus W., Oberhettinger F., Tricomi F., Higher Transcendental Functions, Bateman Manuscript Project, 2, (1966)
[8]  
Gazzola F., Grunau H.C., Sweers G., Polyharmonic Boundary Value Problems: Positivity Preserving and Nonlinear Higher Order Elliptic Equations in Bounded Domains, (2010)
[9]  
Kal'menov T.S., Koshanov B.D., Representation for the Green’s function of the Dirichlet problem for polyharmonic equations in a ball, Sib. Math. J., 49, (2008)
[10]  
Kal'menov T.S., Suragan D., On a new method for constructing the Green function of the Dirichlet problem for the polyharmonic equation, Differ. Equ., 48, (2012)
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