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J. Sib. Fed. Univ. Math. Phys., 2020, Volume 13, Issue 6, Pages 755–762 (Mi jsfu879)  

Mixed biharmonic Dirichlet–Neumann problem in exterior domains

Hovik A. Matevossianab

a Federal Research Center "Computer Science and Control" RAS, Moscow, Russian Federation
b Moscow Aviation Institute (National Research University), Moscow, Russian Federation

Abstract: We study the unique solvability of the mixed Dirichlet–Neumann problem for the biharmonic equation in the exterior of a compact set under the assumption that solutions of this problem have bounded Dirichlet integrals with the weight $|x|^a$. Depending on the value of the parameter $a$, we obtained uniqueness (non-uniqueness) theorems of the problem and present exact formulas for the dimension of the space of solutions of the mixed Dirichlet–Neumann problem.

Keywords: biharmonic operator, Dirichlet–Neumann problem, weighted Dirichlet integral.

DOI: https://doi.org/10.17516/1997-1397-2020-13-6-755-762

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Bibliographic databases:

UDC: 517.95
Received: 17.09.2019
Received in revised form: 04.06.2020
Accepted: 17.10.2020
Language:

Citation: Hovik A. Matevossian, “Mixed biharmonic Dirichlet–Neumann problem in exterior domains”, J. Sib. Fed. Univ. Math. Phys., 13:6 (2020), 755–762

Citation in format AMSBIB
\Bibitem{Mat20}
\by Hovik~A.~Matevossian
\paper Mixed biharmonic Dirichlet--Neumann problem in exterior domains
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2020
\vol 13
\issue 6
\pages 755--762
\mathnet{http://mi.mathnet.ru/jsfu879}
\crossref{https://doi.org/10.17516/1997-1397-2020-13-6-755-762}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000606215300009}


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  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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