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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 1, Pages 132–150 (Mi zvmmf11024)  

This article is cited in 1 scientific paper (total in 1 paper)

Class of Neumann-type problems for the polyharmonic equation in a ball

V. V. Karachik

South Ural State University, Chelyabinsk, 454080 Russia

Abstract: A set of necessary solvability conditions for the class ${\mathcal{N}}_{k}$ of Neumann-type problems for the polyharmonic equation with a polynomial right-hand side in the unit ball is obtained. These conditions have the form of the orthogonality of homogeneous harmonic polynomials to linear combinations of boundary functions with coefficients from the Neumann integer triangle perturbed by certain derivatives of the right-hand side of the equation.

Key words: Neumann-type problems, polyharmonic equation, necessary solvability conditions.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 02.A03.21.0011
This work was supported by the Government of the Russian Federation, Resolution no. 211 of March 16, 2013, and Agreement no. 02.A03.21.0011.


DOI: https://doi.org/10.31857/S0044466919120123


English version:
Computational Mathematics and Mathematical Physics, 2020, 60:1, 144–162

Bibliographic databases:

UDC: 517.958
Received: 18.02.2019
Revised: 18.02.2019
Accepted:18.09.2019

Citation: V. V. Karachik, “Class of Neumann-type problems for the polyharmonic equation in a ball”, Zh. Vychisl. Mat. Mat. Fiz., 60:1 (2020), 132–150; Comput. Math. Math. Phys., 60:1 (2020), 144–162

Citation in format AMSBIB
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\pages 144--162
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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, “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 вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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