Zapiski Nauchnykh Seminarov POMI
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Zap. Nauchn. Sem. POMI:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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
Full-text PDF (220 kB)
References:
PDF
HTML
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}
Linking options:
  • https://www.mathnet.ru/eng/znsl6028
  • https://www.mathnet.ru/eng/znsl/v426/p12
    • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Записки научных семинаров ПОМИ
    Statistics & downloads:
    Abstract page:281
    Full-text PDF :119
    References:37
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024