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The Behavior of a Capillary Surface for Small Bond Number

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Variational Methods for Free Surface Interfaces

Abstract

The boundary value problem

$$\begin{array}{lc}\text{div}(Tu) = \kappa u & \text{in} \Omega \\ Tu \cdot v = \cos\gamma & \text{on} \Sigma = \partial \Omega\end{array}$$
(1)

determines the height u(x) of a capillary surface. Here κ is a positive constant, Ω is a bounded domain in R n, v is the exterior normal on Σ, and Tu is the vector operator

$$Tu = \frac{\nabla u}{\sqrt{1 + |\nabla u|^2}}.$$

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References

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Authors
  1. David Siegel
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Editor information

Editors and Affiliations

  1. Lawrence Berkeley Laboratory and Department of Mathematics, University of California, Berkeley, California, 94720, USA

    Paul Concus

  2. Department of Mathematics, Stanford University, Stanford, California, 94305, USA

    Robert Finn

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© 1987 Springer-Verlag New York Inc.

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Siegel, D. (1987). The Behavior of a Capillary Surface for Small Bond Number. In: Concus, P., Finn, R. (eds) Variational Methods for Free Surface Interfaces. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4656-5_12

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  • DOI: https://doi.org/10.1007/978-1-4612-4656-5_12

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-9101-5

  • Online ISBN: 978-1-4612-4656-5

  • eBook Packages: Springer Book Archive

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