A generalization of “Existence and behavior of the radial limits of a bounded capillary surface at a corner”

Julie N. Crenshaw, Alexandra K. Echart and Kirk E. Lancaster

Vol. 292 (2018), No. 2, 355–371

DOI: 10.2140/pjm.2018.292.355

Abstract

The principal 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. 176:1 (1996), 165–194) is extended to the case of a contact angle $\gamma$ which is not bounded away from $0$ and $\pi$ (and depends on position in a bounded domain $\Omega \in {ℝ}^2$ with a convex corner at $\mathcal{O}=\left(0,0\right)$). The lower bound on the size of “side fans” (i.e., Theorem 2 in the above paper) is extended to the case of such contact angles for convex and nonconvex corners.

Keywords

radial limits, capillary surfaces, corners, discontinuities

Mathematical Subject Classification 2010

Primary: 35J93, 58E12

Secondary: 35J60, 53A10

Milestones

Received: 17 January 2017

Revised: 19 June 2017

Accepted: 30 June 2017

Published: 17 October 2017