### 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 language | English |
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Pages (from-to) | 333-355 |

Number of pages | 23 |

Journal | Journal of the Mathematical Society of Japan |

Volume | 57 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jan 1 2005 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

Koiso, M., & Palmer, B. (2005). On a variational problem for soap films with gravity and partially free boundary.

*Journal of the Mathematical Society of Japan*,*57*(2), 333-355. https://doi.org/10.2969/jmsj/1158242062