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Anisotropic capillary surfaces with wetting energy. (English) Zbl 1136.76011
The authors generalize results of T. I. Vogel and R. Finn [Z. Anal. Anwend. 11, No. 1, 3–23 (1992; Zbl 0760.76015)] and M. Athanassenas [Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 26, No. 4, 749–762 (1998; Zbl 0927.76011)] concerning liquid drops between two parallel planes to free anisotropic energies of the type [X]:= Σ F(ν)dΣ, where ν=(ν 1 ,ν 2 ,ν 3 ): ΣS 2 is the Gauss map of X: Σ 3 . The reason for this generalization is that the classical isotropic surface tension must be replaced by an anisotropic one if the materials involved enter a solid or liquid crystal phase. In particular, the paper contains a derivation of the first and second variation of rotationally symmetric anisotropic surface energies and a stability analysis of anisotropic Delaunay surfaces which are equilibria of the problem. The stability analysis is based on the study of eigenvalues of a linear second-order ordinary differential equation associated to the second variation.
76B45Capillarity (surface tension)
76E17Interfacial stability and instability (fluid dynamics)
49Q05Minimal surfaces (calculus of variations)
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