Application of the Almansi formula for constructing polynomial solutions to the Dirichlet problem for a second-order equation

被引：1

作者：

Karachik V.V. ^{[1
]}

机构：

[1] Southern Ural State University, Chelyabinsk, 454080

来源：

Russian Mathematics | 2012年 / 56卷 / 6期

关键词：

Almansi decomposition; Dirichlet problem; Polynomial solutions;

D O I：

10.3103/S1066369X12060035

中图分类号：

学科分类号：

摘要：

We obtain the Almansi decomposition for the second-order partial differential operators with constant coefficients. This decomposition is used for constructing a polynomial solution to the Dirichlet problem. © Allerton Press, Inc., 2012.

引用

页码：20 / 29

页数：9

共 9 条

[1] Almansi E., Sull'Integrazione dell'Equazione Differenziale Δ <sup>2n</sup>u = 0, Ann. Mat. Pura Appl., 2, 3, pp. 1-51, (1899)
[2] Karachik V.V., On one representation of analytic functions by harmonic functions, Matem. Trudy, 10, 2, pp. 142-162, (2007)
[3] Nicolescu M., Probléme de l'Analyticité par Rapport á un Opérateur Linéaire, Stud. Math., 16, pp. 353-363, (1958)
[4] Karachik V.V., On an expansion of almansi type, Matem. Zametki, 83, 3, pp. 370-380, (2008)
[5] Karachik V.V., Normalized system of functions with respect to the laplace operator and its applications, J. of Math. Anal. Appl., 287, 2, pp. 577-592, (2003)
[6] Liu L., Ren G.B., Normalized system for wave and dunkl operators, Taiwanese J. Math., 14, 2, pp. 675-683, (2010)
[7] Karachik V.V., Polynomial solutions to systems of partial differential equations with constant coefficients, Yokohama Math J., 47, 2, pp. 121-142, (2000)
[8] Nikol'skii S.M., The cases when the solution to the boundary problem is polynomial, Dokl. Phys., 366, 6, pp. 746-748, (1999)
[9] Karachik V.V., Construction of polynomial solutions to some boundary-value problems for poisson's equation, Zhurn. Vychisl. Matem. i Matem. Fiz., 51, 9, pp. 1674-1694, (2011)

← 1 →