Regularity of capillary surfaces over domains with corners: borderline case
Luen-Fai Tam · Pacific Journal of Mathematics · 1986
Consider the solutions of capillary surface equation with contact angle boundary condition over domains with corners.It is known that if the corner angle 2a satisfies 0 π/2 where 0 < γ < π/2 is the contact angle, then solutions are regular.It is also known that no regularity holds in case α + γ < τr/2.In this paper we show that solutions are still regular for the borderline case α + γ = π/2 at the corner.