On a Problem in the Calculus of Variations

Resumo

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.