On a variational problem for soap films with gravity and partially free boundary

Miyuki Koiso, Bennett Palmer

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We pose a variational problem for surfaces whose solutions are a geometric model for thin films with gravity which is partially supported by a given contour. The energy functional contains surface tension, a gravitational energy and a wetting energy, and the Euler-Lagrange equation can be expressed in terms of the mean curvature of the surface, the curvatures of the free boundary and a few other geometric quantities. Especially, we study in detail a simple case where the solutions are vertical planar surfaces bounded by two vertical lines. We determine the stability or instability of each solution.

Original languageEnglish
Pages (from-to)333-355
Number of pages23
JournalJournal of the Mathematical Society of Japan
Volume57
Issue number2
DOIs
Publication statusPublished - Jan 1 2005
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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