Journal of Mathematical Sciences

, Volume 214, Issue 3, pp 252–259 | Cite as

On a Problem in the Calculus of Variations


The paper has a scientific-methodical nature. The classical soap film shape (minimal surface) problem is considered, the film being stretched between two parallel coaxial rings. An analytic approach based on the relations to the Sturm–Liouville problem is proposed. An interpretation of the energy terms of the classical Goldschmidt condition is discussed. The appearance of a soliton potential when analyzing the second variation is noticed. Bibliography: 3 titles.


Soliton Minimal Surface Liouville Equation Liouville Theory Liouville Problem 


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  1. 1.
    F. V. Atkinson, Discrete and Continuous Boundary Problems, Academic Press, New York–London (1964).MATHGoogle Scholar
  2. 2.
    G. Arfken, Mathematical Methods for Physicists, Academic Press, New York–London (1966).MATHGoogle Scholar
  3. 3.
    V. S. Buslaev, Calculus of Variations [in Russian], Leningrad State University, Leningrad (1980).Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.St. Petersburg Department of the Steklov Mathematical InstituteSt. PetersburgRussia
  2. 2.St. Petersburg State UniversitySt. PetersburgRussia

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