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Capillary Surfaces in Wedge Domains
Jin-Tzu Chen, Robert Finn and Erich Miersemann
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.