On the behaviour of capillaries at a corner

Erich Miersemann

Vol. 140 (1989), No. 1, 149–153

DOI: 10.2140/pjm.1989.140.149

Abstract

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 2α satisfies 0 < 2α < π and α + γ < π∕2 where 0 ≤ γ < π∕2 is the contact angle between the surface and the container wall then it is shown that the leading term which was discovered by Concus and Finn is equal to the solution up to O(r^𝜀) for an 𝜀 > 0 where r denotes the distance from the corner.

Mathematical Subject Classification 2000

Primary: 35J60

Secondary: 35C20, 76B45, 49F99

Milestones

Received: 15 May 1988

Published: 1 November 1989