On the asymptotic behaviour of capillary surfaces in cusps (Q1881488)

The author obtains very interesting results concerning the rise of a liquid over a cusp. For example, the cross section of two circular cylinders in contact defines such a cusp. If in this special case each radius of the cross section of the cylinders is 1, then the following explicit formula for the rise \(u\) is shown: \(u\sim 2\cos\gamma/(\kappa s^2)\) as \(s\to 0\), where \(\kappa\) is the capillary constant and \(s\) is the distance (in a curvilinear coordinate system) from the corner. The proof of the formulas is based on a maximum principle of Concus and Finn which exploits the special nonlinearity of the problem. There is no counterpart for the linearized problem.