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This article is cited in 7 scientific papers (total in 7 papers)
Polynomial solutions to Dirihlet boundary value problem for the $3$-harmonic equation in a ball
Valery V. Karachik
South Ural State University, Chelyabinsk, Russia
Abstract:
Polynomial solution to Dirihlet boundary value problem for the nonhomogeneous $3$-harmonic equation in a ball with polynomial right-hand side and polynomial boundary data is found.
Keywords:
$3$-harmonic equation, Almansi decomposition, harmonic polynomials, Dirihlet boundary value problem, polynomial solutions.
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UDC:
513.88
Received: 21.03.2012
Received in revised form: 01.04.2012
Accepted: 21.06.2012
Citation:
Valery V. Karachik, “Polynomial solutions to Dirihlet boundary value problem for the $3$-harmonic equation in a ball”, J. Sib. Fed. Univ. Math. Phys., 5:4 (2012), 527–546
Citation in format AMSBIB
\Bibitem{Kar12}
\by Valery~V.~Karachik
\paper Polynomial solutions to Dirihlet boundary value problem for the $3$-harmonic equation in a~ball
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2012
\vol 5
\issue 4
\pages 527--546
\mathnet{http://mi.mathnet.ru/jsfu266}
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http://mi.mathnet.ru/eng/jsfu266 http://mi.mathnet.ru/eng/jsfu/v5/i4/p527
Citing articles on Google Scholar:
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Russian articles,
English articles
This publication is cited in the following articles:
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V. V. Karachik, “On solvability conditions for a Neumann problem for a polyharmonic equation in the unit ball”, J. Appl. Industr. Math., 8:1 (2014), 63–75
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V. V. Karachik, “On the Arithmetic Triangle Arising from the Solvability Conditions for the Neumann Problem”, Math. Notes, 96:2 (2014), 217–227
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V. V. Karachik, “Construction of polynomial solutions to the Dirichlet problem for the polyharmonic equation in a ball”, Comput. Math. Math. Phys., 54:7 (2014), 1122–1143
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I. A. Gulyaschikh, “Razreshimost odnoi zadachi tipa Neimana dlya trigarmonicheskogo uravneniya v share”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 9:3 (2017), 5–12
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B. Kh. Turmetov, “On the solvability of some boundary value problems for the inhomogeneous polyharmonic equation with boundary operators of the Hadamard type”, Differ. Equ., 53:3 (2017), 333–344
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V. V. Karachik, “The Green Function of the Dirichlet Problem for the Triharmonic Equation in the Ball”, Math. Notes, 107:1 (2020), 105–120
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V. V. Karachik, “Usloviya razreshimosti zadachi Neimana $\mathcal{N}_2$ dlya poligarmonicheskogo uravneniya v share”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 12:2 (2020), 13–20
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