Electron. J. Diff. Eqns.,
Vol. 2008(2008), No. 160, pp. 125.
Vertical blow ups of capillary surfaces in
,
Part 2: Nonconvex corners
Thalia Jeffres, Kirk Lancaster
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
and
when
and
(or
)
minimizes
an appropriate functional and the domain has a nonconvex corner.
Sets like
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 ConcusFinn Conjecture for contact angles 0 and
, a
capillary surface in positive gravity in
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
ConcusFinn Conjecture.
Submitted August 3, 2007. Published December 9, 2008.
Math Subject Classifications: 49Q20, 53A10, 76B45.
Key Words: Blowup sets; capillary surface; ConcusFinn conjecture.
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Thalia Jeffres
Department of Mathematics and Statistics
Wichita State University
Wichita, Kansas, 672600033, USA
email: jeffres@math.wichita.edu 

Kirk Lancaster
Department of Mathematics and Statistics
Wichita State University
Wichita, Kansas, 672600033, USA
email: lancaster@math.wichita.edu 
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