Vol. 292, No. 2, 2018

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ISSN: 0030-8730
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
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 γ which is not bounded away from 0 and π (and depends on position in a bounded domain Ω 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 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
Authors
Julie N. Crenshaw
Department of Mathematics, Statistics and Physics
Wichita State University
Wichita, KS
United States
Alexandra K. Echart
Department of Mathematics, Statistics and Physics
Wichita State University
Wichita, KS
United States
Kirk E. Lancaster
Wichita, Kansas
Wichita, KS
United States