Abstract:
For a capillary graph in a vertical cylinder × R R3, the existence of a
reentrant corner P 2 @ makes the determination of the continuity at P
(or the behavior of the radial limits at P) of the solution problematic. Since
continuity is the necessary consequence of the existence of a “central fan” of
radial limits under certain conditions, the determination of necessary and
sufficient conditions for the existence of a central fan is a very important
open question in the mathematical theory of capillarity. Examples by Finn
and Shi suggest that “central fans” may be very rare in the sense that arbitrarily
small perturbations can eliminate them. In this note we obtain
examples of capillary graphs (with zero mean curvature), each of which is
continuous or has a central fan at a reentrant corner.
