A canonical proboscis domain corresponding to contact angle as introduced by Fischer and Finn and later studied by Finn and Leise, has the property that a solution of the capillary problem exists in for contact angle if and only if . 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 . The modification can be effected in such a way that for prescribed the solution height must-physically become infinite when , over a subdomain that includes as large a portion of as desired.
Cite this article
Robert Finn, J. Marek, The Modified Canonical Proboscis. Z. Anal. Anwend. 15 (1996), no. 1, pp. 95–108