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Consider the solution of the capillary surface equation over domains with a corner. It is assumed that the corner is bounded by lines. If the corner angle 2a satisfies 0 0 where r denotes the distance from the corner. We consider the non-parametric capillary problem in presence of gravity over a bounded base domain Ω c R2 with a corner. That means, we seek a surface S: u = u{x), defined over Ω, such that S meets vertical cylinder walls over the boundary dΩ in a prescribed constant angle γ such that the following equations are satisfied, see Finn [3],

On the behaviour of capillaries at a corner