# The Modified Canonical Proboscis

### Robert Finn

Stanford University, USA### Jonathan Marek

Mercer Management Consulting, Lexington, USA

## Abstract

A canonical proboscis domain $Ω$ corresponding to contact angle as introduced $γ_{0}$ by Fischer and Finn and later studied by Finn and Leise, has the property that a solution of the capillary problem exists in $Ω$ for contact angle $γ$ if and only if $∣γ–2π ∣<∣γ_{0}–2π ∣$. 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 $γ_{0}$. The modification can be effected in such a way that for prescribed $ϵ>0$ the solution height must-physically become infinite when $∣γ–2π ∣>∣γ_{0}–ϵ–2π ∣$, over a subdomain that includes as large a portion of $Ω$ as desired.

## Cite this article

Robert Finn, Jonathan Marek, The Modified Canonical Proboscis. Z. Anal. Anwend. 15 (1996), no. 1, pp. 95–108

DOI 10.4171/ZAA/690