Vol. 224, No. 2, 2006

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David Siegel

Abstract

An iterative method is introduced for approximating symmetric capillary surfaces which makes use of the known exact volume. For the interior and annular problems this leads to upper and lower bounds at the center or inner boundary and at the outer boundary, and to an asymptotic expansion in powers of the Bond number. For the exterior problem we determine the leading order asymptotics of the boundary height as the Bond number tends to zero, obtaining a result first proved by B. Turkington.

Keywords

capillarity, symmetric capillary surface, exterior problem, approximation, asymptotics

Mathematical Subject Classification

Primary: 76B45, 34E05, 34B15, 34B40

Authors
David Siegel
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1