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dc.contributor.authorJeffres, Thalia D.
dc.contributor.authorLancaster, Kirk E.
dc.identifier.citationJeffres, 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.en_US
dc.description.abstractThe 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.en_US
dc.publisherTexas State University - San Marcosen_US
dc.relation.ispartofseriesElectronic Journal of Differential Equations;v.2008 no.160
dc.subjectBlow-up sets
dc.subjectCapillary surface
dc.subjectConcus-Finn conjecture
dc.subject.classificationDifferential equations
dc.titleVertical blow ups of capillary surfaces in R3, part 2: nonconvex cornersen_US
dc.description.versionPeer reviewed
dc.rights.holderThe journal distributed under CC BY-NC license

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