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.
Publié le : 2005-04-14
Classification:
variational problem,
stability of critical point,
partially free boundary,
soap film,
gravitational energy,
49Q10,
58E10,
53C42
@article{1158242062,
author = {KOISO, Miyuki and PALMER, Bennett},
title = {On a variational problem for soap films with gravity and partially free boundary},
journal = {J. Math. Soc. Japan},
volume = {57},
number = {4},
year = {2005},
pages = { 333-355},
language = {en},
url = {http://dml.mathdoc.fr/item/1158242062}
}
KOISO, Miyuki; PALMER, Bennett. On a variational problem for soap films with gravity and partially free boundary. J. Math. Soc. Japan, Tome 57 (2005) no. 4, pp. 333-355. http://gdmltest.u-ga.fr/item/1158242062/