### Abstract

We study the stability of surfaces trapped between two parallel planes with free boundary on these planes. The energy functional consists of anisotropic surface energy, wetting energy, and line tension. Equilibrium surfaces are surfaces with constant anisotropic mean curvature. We study the case where the Wulff shape is of "product form", that is, its horizontal sections are all homothetic and have a certain symmetry. Such an anisotropic surface energy is a natural generalization of the area of the surface. In particular, we study the stability of parts of anisotropic Delaunay surfaces which arise as equilibrium surfaces. They are surfaces of the same product form of the Wulff shape. We show that, for these surfaces, the stability analysis can be reduced to the case where the surface is axially symmetric and the functional is replaced by an appropriate axially symmetric one. Moreover, we obtain necessary and sufficient conditions for the stability of anisotropic sessile drops.

Original language | English |
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Pages (from-to) | 555-587 |

Number of pages | 33 |

Journal | Calculus of Variations and Partial Differential Equations |

Volume | 43 |

Issue number | 3-4 |

DOIs | |

Publication status | Published - Mar 2012 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

### Cite this

*Calculus of Variations and Partial Differential Equations*,

*43*(3-4), 555-587. https://doi.org/10.1007/s00526-011-0423-x

**Equilibria for anisotropic surface energies with wetting and line tension.** / Koiso, Miyuki; Palmer, Bennett.

Research output: Contribution to journal › Article

*Calculus of Variations and Partial Differential Equations*, vol. 43, no. 3-4, pp. 555-587. https://doi.org/10.1007/s00526-011-0423-x

}

TY - JOUR

T1 - Equilibria for anisotropic surface energies with wetting and line tension

AU - Koiso, Miyuki

AU - Palmer, Bennett

PY - 2012/3

Y1 - 2012/3

N2 - We study the stability of surfaces trapped between two parallel planes with free boundary on these planes. The energy functional consists of anisotropic surface energy, wetting energy, and line tension. Equilibrium surfaces are surfaces with constant anisotropic mean curvature. We study the case where the Wulff shape is of "product form", that is, its horizontal sections are all homothetic and have a certain symmetry. Such an anisotropic surface energy is a natural generalization of the area of the surface. In particular, we study the stability of parts of anisotropic Delaunay surfaces which arise as equilibrium surfaces. They are surfaces of the same product form of the Wulff shape. We show that, for these surfaces, the stability analysis can be reduced to the case where the surface is axially symmetric and the functional is replaced by an appropriate axially symmetric one. Moreover, we obtain necessary and sufficient conditions for the stability of anisotropic sessile drops.

AB - We study the stability of surfaces trapped between two parallel planes with free boundary on these planes. The energy functional consists of anisotropic surface energy, wetting energy, and line tension. Equilibrium surfaces are surfaces with constant anisotropic mean curvature. We study the case where the Wulff shape is of "product form", that is, its horizontal sections are all homothetic and have a certain symmetry. Such an anisotropic surface energy is a natural generalization of the area of the surface. In particular, we study the stability of parts of anisotropic Delaunay surfaces which arise as equilibrium surfaces. They are surfaces of the same product form of the Wulff shape. We show that, for these surfaces, the stability analysis can be reduced to the case where the surface is axially symmetric and the functional is replaced by an appropriate axially symmetric one. Moreover, we obtain necessary and sufficient conditions for the stability of anisotropic sessile drops.

UR - http://www.scopus.com/inward/record.url?scp=85028114818&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85028114818&partnerID=8YFLogxK

U2 - 10.1007/s00526-011-0423-x

DO - 10.1007/s00526-011-0423-x

M3 - Article

AN - SCOPUS:85028114818

VL - 43

SP - 555

EP - 587

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

SN - 0944-2669

IS - 3-4

ER -