Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 2014, Volume 14, Issue 4(2), Pages 550–558
This article is cited in 2 scientific papers (total in 2 papers)
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
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.
Polyharmonic equation, polyharmonic polynomials, Dirichlet problem.
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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
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\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.
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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
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