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

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概要

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• 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.

• 社団法人 日本数学会の論文
• 2005-04-01

著者

• Palmer Bennett

  Department Of Mathematics Idaho State University

• Koiso Miyuki

  Department Of Mathematics Nara Women's University

• Koiso Miyuki

  Department Of Mathematics Kyotouniversity Ofeducation

• Palmer Bennett

  Department Of Mathematical Sciences University Of Durham

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