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Mat. Zametki, 2017, Volume 102, Issue 1, Pages 39–51 (Mi mz11035)  

This article is cited in 5 scientific papers (total in 5 papers)

On the Dirichlet–Riquier Problem for Biharmonic Equations

V. V. Karachika, B. T. Torebekb

a South Ural State University, Chelyabinsk
b Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science, Republic of Kazakhstan

Abstract: The existence of a solution of the Dirichlet–Riquier problem for a homogeneous biharmonic equation in the unit ball with boundary operators up to third order containing normal derivatives and the Laplacian is studied. Existence theorems for the solutions of the problem are proved.

Keywords: biharmonic equation, boundary-value problem, normal derivatives, Laplacian.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 02.A03.21.0011
This work was supported in part by the Government of the Russian Federation (decree no. 211 of 16.03.2013) under contract no. 02. A03.21.0011.

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/mzm11035

Full text: PDF file (504 kB)
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English version:
Mathematical Notes, 2017, 102:1, 31–42

Bibliographic databases:

UDC: 517.956.223
Received: 15.12.2015
Revised: 01.09.2016

Citation: V. V. Karachik, B. T. Torebek, “On the Dirichlet–Riquier Problem for Biharmonic Equations”, Mat. Zametki, 102:1 (2017), 39–51; Math. Notes, 102:1 (2017), 31–42

Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm11035
  • http://mi.mathnet.ru/eng/mz/v102/i1/p39

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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, “Zadacha tipa Neimana dlya poligarmonicheskogo uravneniya v share”, Chelyab. fiz.-matem. zhurn., 2:4 (2017), 420–429  mathnet  mathscinet  elib
    2. V. V. Karachik, “Riquier–Neumann problem for the polyharmonic equation in a ball”, Differ. Equ., 54:5 (2018), 648–657  crossref  crossref  mathscinet  isi  elib  elib  scopus
    3. V. V. Karachik, B. Kh. Turmetov, “On the Green's function for the third boundary value problem”, Siberian Adv. Math., 29:1 (2019), 32–43  mathnet  crossref  crossref  elib
    4. Karachik V.V. Turmetov B.K., “On Green'S Function of the Robin Problem For the Poisson Equation”, Adv. Pure Appl. Math., 10:3 (2019), 203–213  crossref  isi
    5. 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
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