#### Vol. 292, No. 2, 2018

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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 $\gamma$ 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 $\mathsc{O}=\left(0,0\right)$). 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