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

Miyuki Koiso, Bennett Palmer

研究成果: Contribution to journalArticle査読

3 被引用数 (Scopus)

抄録

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.

本文言語英語
ページ(範囲)333-355
ページ数23
ジャーナルJournal of the Mathematical Society of Japan
57
2
DOI
出版ステータス出版済み - 2005
外部発表はい

All Science Journal Classification (ASJC) codes

  • 数学 (全般)

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