Regularity of capillary surfaces over domains with corners: borderline case

Luen-Fai Tam

Vol. 124 (1986), No. 2, 469–482

DOI: 10.2140/pjm.1986.124.469

Abstract

Consider the solutions of capillary surface equation with contact angle boundary condition over domains with corners. It is known that if the corner angle 2α satisfies 0 < 2α < π and α + γ > 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 < π∕2. In this paper we show that solutions are still regular for the borderline case α + γ = π∕2 at the corner.

Mathematical Subject Classification 2000

Primary: 49F10, 49F10

Secondary: 53A10

Milestones

Received: 7 February 1984

Published: 1 October 1986