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CATEGORIES:Geometric Analysis and Partial Differential Equati
ons seminar
SUMMARY:$C^{1\, \\alpha}$ theory for the prescribed mean c
urvature equation with Dirichlet data - Theodora B
ourni (AEI\, Potsdam)
DTSTART;TZID=Europe/London:20090223T160000
DTEND;TZID=Europe/London:20090223T170000
UID:TALK16535AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/16535
DESCRIPTION:I will discuss regularity of solutions of the pres
cribed mean \ncurvature equation over a general d
omain that do not necessarily \nattain the given
boundary data. The work of E.Giusti and others\,
\nestablishes a very general existence theory of s
olutions with \n"unattained Dirichlet data" by mi
nimizing an appropriately defined \nfunctional\,
which includes information about the boundary data
. We can naturally associate to such a solution a
current\, which inherits a natural minimizing pr
operty. The main goal is to show that its support
is a $C{1\,\\alpha}$ manifold-with-boundary\, wit
h boundary equal to the prescribed boundary data\
, provided that both the initial domain and the p
rescribed boundary data are of class $C^{1\,\\alph
a}$.\n\nFurthermore\, as a consequence\, I will di
scuss some interesting results about the trace of
such a solution\; in particular for a large class
of boundary data with jump discontinuities\, the
trace has a jump discontinuity along which it at
taches to the vertical part of the prescribed bou
ndary.\n\n
LOCATION:CMS\, MR13
CONTACT:Prof. Mihalis Dafermos
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