Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 57, Number 2 (2005), 333-355.
On a variational problem for soap films with gravity and partially free boundary
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.
J. Math. Soc. Japan, Volume 57, Number 2 (2005), 333-355.
First available in Project Euclid: 14 September 2006
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 49Q10: Optimization of shapes other than minimal surfaces [See also 90C90]
Secondary: 58E10: Applications to the theory of geodesics (problems in one independent variable) 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
KOISO, Miyuki; PALMER, Bennett. On a variational problem for soap films with gravity and partially free boundary. J. Math. Soc. Japan 57 (2005), no. 2, 333--355. doi:10.2969/jmsj/1158242062. https://projecteuclid.org/euclid.jmsj/1158242062