On a singular behavior of capillary surfaces

Robert Finn; Darren Lee
December 2003
Calculus of Variations & Partial Differential Equations;Dec2003, Vol. 19 Issue 1, p95
Academic Journal
Mario Miranda raised the question, whether a capillary tube of section ${\cal D}_{0}$ in an infinite bath under a uniform downward gravity field always raises liquid higher over its section than does a tube of the same material and section ${\cal D}_1 \supset \supset {\cal D}_0$ . Finn and Kosmodem?yanskii, Jr. recently gave conditions under which a negative answer is obtained for all gravity small enough; they gave also an example in which ${\cal D}_0$ is a disk and in which the answer changes in a discontinuous way, for fixed ${\cal D}_1$ and differentiable change of $\partial {\cal D}_0$ . In the present work we characterize the most general convex ${\cal D}_1$ for which such a discontinuous change can occur.


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