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Existence and non existence of capillary surfaces

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Abstract

A general criterion for existence of solutions of the capillary equation, introduced by Concus and Finn [1] and by Giusti [7], is shown to be equivalent to the question of existence of certain vector fields. The result is applied to particular boundary configurations, and it is shown that in some cases the local “corner condition” of [1] is both necessary and sufficient in the global configuration. In other situations a different kind of unstable dependence on the boundary geometry appears, that could not have been predicted by previous results.

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References

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Authors and Affiliations

  1. Department of Mathematics, Stanford University, 94 305, Stanford, California, USA

    Robert Finn

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  1. Robert Finn
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Dedicated to Hans Lewy and Charles B. Morrey, Jr.

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Finn, R. Existence and non existence of capillary surfaces. Manuscripta Math 28, 1–11 (1979). https://doi.org/10.1007/BF01647961

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  • DOI: https://doi.org/10.1007/BF01647961

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