Vol. 125, No. 2, 1986

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On existence criteria for capillary free surfaces without gravity

Luen-Fai Tam

Vol. 125 (1986), No. 2, 469–485

Consider a cylinder of homogenous material closed at one end by a base of general cross section Ω and partly filled with liquid. We want to find conditions under which in the absence of gravity the liquid can cover Ω and is in mechanical equilibrium.

If the liquid can cover Ω, then the liquid surface is a graph over the base. In general, the surface has constant mean curvature and makes constant angle with the bounding wall. Even if Ω is convex analytic, such a surface may not exist. However, it is the case when Ω is piecewise smooth that interests us. In this case, the interior angles at the corners play an important role. It turns out that the existence of the liquid surface as a graph over the base can be characterized by the nonexistence of a certain subsidiary variational problem.

Mathematical Subject Classification 2000
Primary: 49F22, 49F22
Secondary: 35J65, 53A10, 58E12
Received: 2 September 1985
Published: 1 December 1986
Luen-Fai Tam