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Zapiski Nauchnykh Seminarov POMI, 2014, Volume 426, Pages 12–22 (Mi znsl6028)  
On a calculus of variations problem

M. I. Belishevab, A. V. Ivanova

a St. Petersburg State University, St. Petersburg, Russia
b St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences, St. Petersburg, Russia
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Abstract: The paper is of scientific-methodical character. The classical soap film shape (minimal surface) problem is considered, the film being stretched between two parallel coaxial rings. An analytical approach based on relations to the Sturm–Liouville problem is proposed. An energy terms interpretation of the classical Goldschmidt condition is discussed. Appearance of the soliton potential in course of the second variation analysis is noticed.
Key words and phrases: soap film shape (minimal surface) problem, critical case, Goldschmidt condition, soliton potential.
Received: 30.09.2014
English version:
Journal of Mathematical Sciences (New York), 2016, Volume 214, Issue 3, Pages 252–259
DOI: https://doi.org/10.1007/s10958-016-2774-5
Bibliographic databases:
Document Type: Article
UDC: 517.972.4+517.972.6
Language: Russian
Citation: M. I. Belishev, A. V. Ivanov, “On a calculus of variations problem”, Mathematical problems in the theory of wave propagation. Part 44, Zap. Nauchn. Sem. POMI, 426, POMI, St. Petersburg, 2014, 12–22; J. Math. Sci. (N. Y.), 214:3 (2016), 252–259
Citation in format AMSBIB
\Bibitem{BelIva14}
\by M.~I.~Belishev, A.~V.~Ivanov
\paper On a~calculus of variations problem
\inbook Mathematical problems in the theory of wave propagation. Part~44
\serial Zap. Nauchn. Sem. POMI
\yr 2014
\vol 426
\pages 12--22
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6028}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3485302}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 214
\issue 3
\pages 252--259
\crossref{https://doi.org/10.1007/s10958-016-2774-5}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84960461872}
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