The Behavior of a Capillary Surface for Small Bond Number

David Siegel

A chapter in Variational Methods for Free Surface Interfaces, 1987, pp 109-113 from Springer

Abstract: Abstract The boundary value problem 1 $$\begin{array}{lc}\text{div}(Tu) = \kappa u & \text{in} \Omega \\ Tu \cdot v = \cos\gamma & \text{on} \Sigma = \partial \Omega\end{array}$$ 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 $$Tu = \frac{\nabla u}{\sqrt{1 + |\nabla u|^2}}.$$

Date: 1987
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DOI: 10.1007/978-1-4612-4656-5_12

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