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 coeficients of this expansion are independent of the particular solution considered.

Keywords

capillarity, mean curvature, corner behavior, comparison method

Mathematical Subject Classification

Primary: 76B45

Secondary: 53A10, 49Q10

Authors