MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Singular solutions of the capillary problem

Robert Finn and Robert Weston Neel


The problem of determining the surface interface of fluid partly filling a semi-infinite capillary tube closed at one end is considered, in the absence of gravity. It is known that solutions of the formal equations for a solution as a graph covering the base do not in general exist. In this paper it is shown that whenever smooth solutions fail to exist there will nevertheless exist a solution in a singular sense suggested by physical intuition. In some configurations of particular interest, the procedure leads to unique determination of the singular solution. However, uniqueness cannot in general be expected, as is shown by example. Further examples show a) that singular solutions may appear also when smooth solutions exist, and b) they may fail to occur in that case, depending on the particular geometry.

MSC Codes:
76B45, 53A10, 53C80, 49Q10, 35J60, 35B65

Related publications

1999 Repository Open Access
Robert Finn and Robert Weston Neel

C-singular solutions of the capillary problem

In: Journal für die reine und angewandte Mathematik (Crelle's Journal), 512 (1999), pp. 1-25