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# Zeitschrift für Analysis und ihre Anwendungen

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**Volume 15, Issue 1, 1996, pp. 95–108**

**DOI: 10.4171/ZAA/690**

Published online: 1996-03-31

The Modified Canonical Proboscis

Robert Finn^{[1]}and J. Marek

^{[2]}(1) Stanford University, USA

(2) Mercer Management Consulting, Lexington, USA

A canonical proboscis domain $\Omega$ corresponding to contact angle as introduced $\gamma_0$ by Fischer and Finn and later studied by Finn and Leise, has the property that a solution of the capillary problem exists in $\Omega$ for contact angle $\gamma$ if and only if $| \gamma – \frac{\pi}{2}| < | \gamma_0 – \frac{\pi}{2}|$. We show in this paper that every such domain can be modified so as to yield the existence of a bounded solution also at the angle $\gamma_0$. The modification can be effected in such a way that for prescribed $\epsilon > 0$ the solution height must-physically become infinite when $| \gamma – \frac{\pi}{2}| > |\gamma_0 – \epsilon – \frac{\pi}{2}|$, over a subdomain that includes as large a portion of $\Omega$ as desired.

*Keywords: *Capillarity, contact angle, mean curvature, canonical proboscis, subsidiary variational problem

Finn Robert, Marek J.: The Modified Canonical Proboscis. *Z. Anal. Anwend.* 15 (1996), 95-108. doi: 10.4171/ZAA/690