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Sibirskii Matematicheskii Zhurnal, 2021, Volume 62, Number 3, Pages 595–602
DOI: https://doi.org/10.33048/smzh.2021.62.311 (Mi smj7580) 		 
On stable extremals of the potential energy functional

N. M. Poluboyarova

Volgograd State University, Volgograd, Russia
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DOI: https://doi.org/10.33048/smzh.2021.62.311
Abstract: We study the problem of the stability of the extremals of the potential energy functional. By the stability of an extremal surface we mean the sign-definiteness of its second variation. For estimating the second variation of the functional, we use the properties of the eigenvalues of symmetric matrices. Also, we prove an analog of Alexandrov's Theorem on the variational property of a sphere.
Keywords: variation of a functional, instability of a surface, stability of a surface, potential energy functional, area-type functional, extremal surface.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2019-1613
The author was supported by the Mathematical Center in Akademgorodok under Agreement No. 075–15–2019–1613 with the Ministry of Science and Higher Education of the Russian Federation.
Received: 12.11.2020
Revised: 23.03.2021
Accepted: 14.04.2021
English version:
Siberian Mathematical Journal, 2021, Volume 62, Issue 3, Pages 482–488
DOI: https://doi.org/10.1134/S0037446621030113
Bibliographic databases:
Document Type: Article
UDC: 514.752+514.764.274+517.97
Language: Russian
Citation: N. M. Poluboyarova, “On stable extremals of the potential energy functional”, Sibirsk. Mat. Zh., 62:3 (2021), 595–602; Siberian Math. J., 62:3 (2021), 482–488
Citation in format AMSBIB
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    		Сибирский математический журнал Siberian Mathematical Journal
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