A Generalization of "Existence and Behavior of the Radial Limits of a Bounded Capillary Surface at a Corner"

Abstract

The principle existence theorem (i.e. Theorem 1) of "Existence and Behavior of the Radial Limits of a Bounded Capillary Surface at a Corner" (Pacific J. Math. Vol. 176, No. 1 (1996), is extended to the case of a contact angle γ which is not bounded away from 0 and π (and depends on position in a bounded domain Ω ∈ IR 2 with a convex corner at O = (0, 0)). The lower bound on the size of "side fans" (i.e. Theorem 2 in the above paper) is extended to case of such contact angles for convex and nonconvex corners.