On a calculus of variations problem
Mathematical Physics
2016-03-21 v1 math.MP
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.
Keywords
Cite
@article{arxiv.1603.05874,
title = {On a calculus of variations problem},
author = {Mikhail I. Belishev and Aleksandr V. Ivanov},
journal= {arXiv preprint arXiv:1603.05874},
year = {2016}
}