Regularity of capillary surfaces over domains with corners: Borderline case
Consider the solutions of the capillary surface equation with contact angle boundary condition over domains with corners. It is known that if the corner angle \(2\alpha\) satisfies \(0<2\alpha <\pi\) and \(\alpha +\gamma >\pi /2\) where \(0<\gamma \leq \pi /2\) is the contact angle, then solutions are regular. It is also known that no regularity holds in case \(\alpha +\gamma \leq \pi /2\). In this paper we show that solutions are still regular for the borderline case \(\alpha +\gamma =\pi /2\) at the corner.
scientific article; zbMATH DE number 3975756