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J. Sib. Fed. Univ. Math. Phys., 2012, Volume 5, Issue 4, Pages 527–546 (Mi jsfu266)  

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.

Full text: PDF file (248 kB)
References: PDF file   HTML file
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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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  mathnet  crossref  mathscinet
    2. V. V. Karachik, “On the Arithmetic Triangle Arising from the Solvability Conditions for the Neumann Problem”, Math. Notes, 96:2 (2014), 217–227  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. 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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. 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  mathnet  crossref  elib
    5. 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  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    6. V. V. Karachik, “The Green Function of the Dirichlet Problem for the Triharmonic Equation in the Ball”, Math. Notes, 107:1 (2020), 105–120  mathnet  crossref  crossref  isi  elib
    7. 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  mathnet  crossref
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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