A generalization of “Existence and behavior of the radial limits of a bounded capillary surface at a corner”
Julie Crenshaw, Alexandra K. Echart, Kirk Eugene Lancaster · Pacific Journal of Mathematics · 2017
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), 165-194) 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 $Ω\in {\bf R}^{2}$ with a convex corner at ${\cal O}=(0,0)$). 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.