Vertical blow ups of capillary surfaces in R3, part 2: nonconvex corners

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Authors
Jeffres, Thalia D.
Lancaster, Kirk E.
Advisors
Issue Date
2008-12
Type
Article
Keywords
Blow-up sets , Capillary surface , Concus-Finn conjecture
Research Projects
Organizational Units
Journal Issue
Citation
Jeffres, Thalia and Kirk Lancaster; Vertical blow ups of capillary surfaces in R3, Part 2: Nonconvex corners. Electronic Journal of Differential Equations. Vol. 2008(2008), No. 160, pp. 1-25.
Abstract

The goal of this note is to continue the investigation started in Part One of the structure of “blown up” sets of the form P × R and N × R when P,N R2 and P (or N) minimizes an appropriate functional and the domain has a nonconvex corner. Sets like P × R can be the limits of the blow ups of subgraphs of solutions of capillary surface or other prescribed mean curvature problems, for example. Danzhu Shi recently proved that in a wedge domain whose boundary has a nonconvex corner at a point O and assuming the correctness of the Concus-Finn Conjecture for contact angles 0 and , a capillary surface in positive gravity in × R must be discontinuous under certain conditions. As an application, we extend the conclusion of Shi’s Theorem to the case where the prescribed mean curvature is zero without any assumption about the Concus-Finn Conjecture.

Table of Contents
Description
Publisher
Texas State University - San Marcos
Journal
Book Title
Series
Electronic Journal of Differential Equations;v.2008 no.160
PubMed ID
DOI
ISSN
1072-6691
EISSN