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Moon Surfaces, and Boundary Behaviour of Capillary Surfaces for Perfect Wetting and Non‐Wetting
Author(s) -
Finn Robert
Publication year - 1988
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-57.3.542
Subject(s) - wetting , capillary action , boundary (topology) , mathematical proof , mathematics , geometry , surface (topology) , character (mathematics) , mathematical analysis , materials science , composite material
The existence of a class of capillary surfaces, corresponding to perfect wetting and perfect non‐wetting on adjacent circular boundary arcs, in the absence of gravity, is proved. The surfaces are shown to achieve the prescribed (extremal) data strictly at interior points of the boundary arcs, and to be discontinuous at the juncture points. The estimates on boundary behaviour are explicit, and apply in general to capillary surfaces that achieve extremal data locally. They are in some ways the best possible. The proofs are based on extensions of known comparison principles and on their use in a new setting, leading to results of a different character than have previously been obtained by such methods.