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Vertical blow ups of capillary surfaces in R3, part 2: nonconvex corners
Jeffres, Thalia D. Lancaster, Kirk E.
Jeffres, Thalia D.
Lancaster, Kirk E.
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2008-12
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Article
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Blow-up sets,Capillary surface,Concus-Finn conjecture
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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.
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Texas State University - San Marcos
Journal
Electronic Journal of Differential Equations
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1072-6691