Abstract
We study the stability of capillary surfaces for anisotropic energies having boundaries supported in horizontal planes. A wetting energy term for the surface to plane interface is included.
Similar content being viewed by others
References
Athanassenas M. (1987). A variational problem for constant mean curvature surfaces with free boundary. J. Reine Angew. Math. 377: 97–107
Barbosa J.L. and Do Carmo M. (1984). Stability of hypersurfaces with constant mean curvature. Math. Z. 185: 339–353
Brothers J.E. and Morgan F. (1994). The isoperimetric theorem for general integrands. Michigan Math. J. 41: 419–431
Courant, R., Hilbert, D.: Methods of Mathematical Physics, Vol. 1, Interscience Publishers, Inc., New York, N.Y., 1953
Gilbarg, D., Trudinger, N.S.: Elliptic Partial Differential Equations of Second Order, 2nd edn. Grundlehren der mathematischen Wissenschaften 224. Springer, Berlin Heidelberg New York (1983)
Hopf, H.: Differential geometry in the Large, 2nd edn. Lecture Notes in Mathematics, vol. 1000, Springer, Berlin Heidelberg New York (1989)
Koiso M. (1986). Symmetry of hypersurfaces of constant mean curvature with symmetric boundary. Math. Zeit. 191: 567–574
Koiso M. (2002). Deformation and stability of surfaces with constant mean curvature. Tohoku Math. J. (2) 54: 145–159
Koiso M. and Palmer B. (2005). On a variational problem for soap films with gravity and partially free boundary. J. Math. Soc. Jpn. 57: 333–355
Koiso M. and Palmer B. (2005). Geometry and stability of surfaces with constant anisotropic mean curvature. Ind. Univ. Math. J. 54: 1817–1852
Koiso M. and Palmer B. (2006). Stability of anisotropic capillary surfaces between two parallel planes. Calcul. Vari. Partial Differential Equations 25: 275–298
Vogel T.I. (1987). Stability of a liquid drop trapped between two parallel planes. SIAM J. Appl. Math. 47: 516–525
Vogel T.I. (1989). Stability of a liquid drop trapped between two parallel planes II, general contact angles. SIAM J. Appl. Math. 49: 1009–1028
Winterbottom W.L. (1967). Equilibrium shape of a small particle in contact with a foreign substrate. Acta Metal. 15: 303–310
Zhou L. (1997). On stability of a catenoidal liquid bridge. Pacific J. Math. 178: 185–198
Author information
Authors and Affiliations
Corresponding author
Additional information
The first author is partially supported by Grant-in-Aid for Scientific Research (C) No. 16540195 of the Japan Society for the Promotion of Science.
Rights and permissions
About this article
Cite this article
Koiso, M., Palmer, B. Anisotropic capillary surfaces with wetting energy. Calc. Var. 29, 295–345 (2007). https://doi.org/10.1007/s00526-006-0066-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00526-006-0066-5