The Modified Canonical Proboscis

  • Robert Finn

    Stanford University, USA
  • J. Marek

    Mercer Management Consulting, Lexington, USA


A canonical proboscis domain Ω\Omega corresponding to contact angle as introduced γ0\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 Ω\Omega for contact angle γ\gamma if and only if γπ2<γ0π2| \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 γ0\gamma_0. The modification can be effected in such a way that for prescribed ϵ>0\epsilon > 0 the solution height must-physically become infinite when γπ2>γ0ϵπ2| \gamma – \frac{\pi}{2}| > |\gamma_0 – \epsilon – \frac{\pi}{2}|, over a subdomain that includes as large a portion of Ω\Omega as desired.

Cite this article

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

DOI 10.4171/ZAA/690