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April, 2005 On a variational problem for soap films with gravity and partially free boundary
Miyuki KOISO, Bennett PALMER
J. Math. Soc. Japan 57(2): 333-355 (April, 2005). DOI: 10.2969/jmsj/1158242062


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.


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Miyuki KOISO. Bennett PALMER. "On a variational problem for soap films with gravity and partially free boundary." J. Math. Soc. Japan 57 (2) 333 - 355, April, 2005.


Published: April, 2005
First available in Project Euclid: 14 September 2006

zbMATH: 1072.49029
MathSciNet: MR2123236
Digital Object Identifier: 10.2969/jmsj/1158242062

Primary: 49Q10
Secondary: 53C42 , 58E10

Keywords: gravitational energy , partially free boundary , soap film , stability of critical point , variational problem

Rights: Copyright © 2005 Mathematical Society of Japan


Vol.57 • No. 2 • April, 2005
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