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Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 2014, Volume 14, Issue 4(2), Pages 550–558 (Mi isu548)  

This article is cited in 2 scientific papers (total in 2 papers)

Mathematics

Green Function of the Dirichlet Boundary Value Problem for Polyharmonic Equation in a Ball Under Polynomial Data

V. V. Karachik

South Ural State University, 76, pr. Lenina, Chelyabinsk, 454080, Russia

Abstract: The classical Dirichlet boundary value problem for the polyharmonic equation in the unit ball is considered. For this problem with polynomial right-hand side and zero boundary data a polynomial solution is constructed. Our approach is based on the Almansi representation of polyharmonic functions and on the previously obtained an explicit representation of the harmonic components, expressed through the given polyharmonic function. In the case of the harmonic equation the known representation of the solution through the Green function is obtained.

Key words: Polyharmonic equation, polyharmonic polynomials, Dirichlet problem.

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Citation: V. V. Karachik, “Green Function of the Dirichlet Boundary Value Problem for Polyharmonic Equation in a Ball Under Polynomial Data”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 14:4(2) (2014), 550–558

Citation in format AMSBIB
\Bibitem{Kar14}
\by V.~V.~Karachik
\paper Green Function of the Dirichlet Boundary Value Problem for Polyharmonic Equation in a Ball Under Polynomial Data
\jour Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform.
\yr 2014
\vol 14
\issue 4(2)
\pages 550--558
\mathnet{http://mi.mathnet.ru/isu548}


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    This publication is cited in the following articles:
    1. M. A. Sadybekov, B. T. Torebek, B. Kh. Turmetov, “Representation of the Green's function of the exterior Neumann problem for the Laplace operator”, Siberian Math. J., 58:1 (2017), 153–158  mathnet  crossref  crossref  isi  elib  elib
    2. V. V. Karachik, “Ob odnom predstavlenii funktsii Grina zadachi Dirikhle dlya bigarmonicheskogo uravneniya v share”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 10:4 (2018), 13–22  mathnet  crossref  elib
  • Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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