A capillary surface with no radial limits

Abstract

In 1996, Kirk Lancaster and David Siegel investigated the existence and behavior of radial limits at a corner of the boundary of the domain of solutions of capillary and other prescribed mean curvature problems with contact angle boundary data. They provided an example of a capillary surface in a unit disk D which has no radial limits at (0, 0) is an element of partial derivative D. In their example, the contact angle, gamma, cannot be bounded away from zero and pi. Here we consider a domain Omega with a convex corner at (0, 0) and find a capillary surface z = f (x, y) in Omega x R which has no radial limits at (0, 0) is an element of partial derivative D such that gamma is bounded away from 0 and pi.