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Vertical blow ups of capillary surfaces in R3, part one: convex corners
Jeffres, Thalia D. Lancaster, Kirk E.
Jeffres, Thalia D.
Lancaster, Kirk E.
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Peer reviewed article
Adobe PDF, 349.72 KB
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Issue Date
2007-11
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Article
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Keywords
Blow-up sets,Capillary surface,Concus-Finn conjecture
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Citation
Jeffres, Thalia and Kirk Lancaster; Vertical blow ups of capillary surfaces in $R^3$, Part 1: convex corners. Electronic Journal of Differential Equations. Vol. 2007(2007), No. 152 pp. 1-24.
Abstract
One technique which is useful in the calculus of variations is that
of “blowing up”. This technique can contribute to the understanding of the
boundary behavior of solutions of boundary value problems, especially when
they involve mean curvature and a contact angle boundary condition. Our goal
in this note is to investigate 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;
sets like P × R can be the limits of the blow ups of subgraphs of solutions of
mean curvature problems, for example. In Part One, we investigate “blown up”
sets when the domain has a convex corner. As an application, we illustrate the
second author’s proof of the Concus-Finn Conjecture by providing a simplified
proof when the mean curvature is zero.
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Open Access article
Publisher
Texas State University - San Marcos
Journal
Electronic Journal of Differential Equations
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1072-6691