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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2018, Volume 152, Pages 103–109 (Mi into354)  
This article is cited in 1 scientific paper (total in 1 paper)

Some Properties of Extremals of the Functional of Potential Energy

N. M. Poluboyarova

Volgograd State University
Full-text PDF (178 kB) Citations (1)
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Abstract: In this paper, we discuss stability and instability criteria for extremal surfaces of a special functional, which is a linear combination of an area-type functional and the functional of volumetric force density. Extremals of such functionals can serve as models of physically equilibrium tents or liquids in potential gravitational fields, so that the problem of their stability or instability is very topical. Our results are based on various geometric properties of surfaces; they are obtained by methods developed by V. M. Miklyukov and V. A. Klyachin.
Keywords: variation of functional, extremal surface, extremal of surface, area-type functional, functional of volumetric force density, functional of potential energy, stability, instability, Jacobi equation, base frequency.
Funding agency Grant number
Russian Foundation for Basic Research 15-41-02479_p_поволжье_a
This work was supported by the Russian Foundation for Basic Research (project No. 15-41-02479 p_povolzhie_a).
English version:
Journal of Mathematical Sciences (New York), 2021, Volume 252, Issue 2, Pages 225–231
DOI: https://doi.org/10.1007/s10958-020-05155-8
Bibliographic databases:
Document Type: Article
UDC: 514.752, 514.764.274, 517.97
MSC: 53A10, 30C70, 31A15
Language: Russian
Citation: N. M. Poluboyarova, “Some Properties of Extremals of the Functional of Potential Energy”, Mathematical physics, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 152, VINITI, Moscow, 2018, 103–109; J. Math. Sci. (N. Y.), 252:2 (2021), 225–231
Citation in format AMSBIB
\Bibitem{Pol18}
\by N.~M.~Poluboyarova
\paper Some Properties of Extremals of the Functional of Potential Energy
\inbook Mathematical physics
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 152
\pages 103--109
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into354}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3903381}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2021
\vol 252
\issue 2
\pages 225--231
\crossref{https://doi.org/10.1007/s10958-020-05155-8}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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