Application of the almansi formula for constructing polynomial solutions to the dirichlet problem for a second-order equation

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• 作者：V. V. Karachik (1) karachik@susu.ru
• 关键词：and phrases Almansi decomposition – ; polynomial solutions – ; Dirichlet problem
• 刊名：Russian Mathematics (Iz VUZ)
• 出版年：2012
• 出版时间：June 2012
• 年：2012
• 卷：56
• 期：6
• 页码：20-29
• 全文大小：530.5 KB
• 参考文献：1. E. Almansi, “Sull’Integrazione dell’Equazione Differenziale Δ2n u = 0,” Ann. Mat. Pura Appl. 2(3), 1–51 (1899).
  2. V. V. Karachik, “On One Representation of Analytic Functions by Harmonic Functions,” Matem. Trudy 10(2), 142–162 (2007).
  3. M. Nicolescu, “Probl茅me de l’Analyticit茅 par Rapport谩 un Op茅rateur Lin茅aire,” Stud. Math. 16, 353–363 (1958).
  4. V. V. Karachik, “On an Expansion of Almansi Type,” Matem. Zametki 83(3), 370–380 (2008).
  5. V. V. Karachik, “Normalized System of Functions with Respect to the Laplace Operator and Its Applications,” J. of Math. Anal. Appl. 287(2), 577–592 (2003).
  6. L. Liu and G. B. Ren, “Normalized System for Wave and Dunkl Operators,” Taiwanese J. Math. 14(2), 675–683 (2010).
  7. V. V. Karachik, “Polynomial Solutions to Systems of Partial Differential Equations with Constant Coefficients,” Yokohama Math. J. 47(2), 121–142 (2000).
  8. S. M. Nikol’skii, “The Cases When the Solution to the Boundary Problem Is Polynomial,” Dokl. Phys. 366(6), 746–748 (1999).
  9. V. V. Karachik, “Construction of Polynomial Solutions to Some Boundary-Value Problems for Poisson’s Equation,” Zhurn. Vychisl. Matem. i Matem. Fiz. 51(9), 1674–1694 (2011).
• 作者单位：1. Southern Ural State University, pr. Lenina 76, Chelyabinsk, 454080 Russia
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：Allerton Press, Inc. distributed exclusively by Springer Science+Business Media LLC
• ISSN：1934-810X

文摘

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.