

Preprint 105/2007
Capillary Surfaces in Wedge Domains
Jin-Tzu Chen, Robert Finn, and Erich Miersemann
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Submission date: 29. Nov. 2007
published in: Pacific journal of mathematics, 236 (2008) 2, p. 283-305
DOI number (of the published article): 10.2140/pjm.2008.236.283
Bibtex
Abstract:
We consider capillary surfaces u(x, y) in a vertical tube whose sections
contain a corner (wedge) with opening 2α, 0 < 2α < 2π, and with
contact angle data γ1, γ2 on the adjacent sides. We interpret geometrically
and improve conditions of Lancaster and Siegel on criteria for
boundedness of solutions. In the case that the solutions are unbounded
we give growth estimates and in the classical case of downward gravity
field a power representation asymptotic to any prescribed order.
The coefficients of this expansion are independent of the particular
solution considered.