Asymptotic expansion at a corner for the capillary problem

Erich Miersemann

Vol. 134 (1988), No. 2, 299–311

DOI: 10.2140/pjm.1988.134.299

Abstract

Consider the solution of capillary surface equation over domains with corners. It is shown that there exists an asymptotic expansion of the solution at the corner 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. It is assumed that the corner is bounded by lines. The leading terms of the expansion are calculated and properties of the remainder are given.

Mathematical Subject Classification 2000

Primary: 35J65

Secondary: 35C20, 53A05

Milestones

Received: 30 April 1987

Published: 1 October 1988