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SUMMARY:$C^{1\, \\alpha}$ theory for the prescribed mean curvature equatio
 n with Dirichlet data - Theodora Bourni (AEI\, Potsdam)
DTSTART:20090223T160000Z
DTEND:20090223T170000Z
UID:TALK16535@talks.cam.ac.uk
CONTACT:Prof. Mihalis Dafermos
DESCRIPTION:I will discuss regularity of solutions of the prescribed mean 
  \ncurvature equation over a general domain that do not necessarily  \natt
 ain the given boundary data. The work of E.Giusti and others\,  \nestablis
 hes a very general existence theory of solutions with  \n"unattained Diric
 hlet data" by minimizing an appropriately defined  \nfunctional\, which in
 cludes information about the boundary data. We can  naturally associate to
  such a solution a current\, which inherits a  natural minimizing property
 . The main goal is to show that its support  is a $C{1\,\\alpha}$ manifold
 -with-boundary\, with boundary equal to the  prescribed boundary data\, pr
 ovided that both the initial domain and  the prescribed boundary data are 
 of class $C^{1\,\\alpha}$.\n\nFurthermore\, as a consequence\, I will disc
 uss some interesting results  about the trace of such a solution\; in part
 icular for a large class of  boundary data with jump discontinuities\, the
  trace has a jump  discontinuity along which it attaches to the vertical p
 art of the  prescribed boundary.\n\n
LOCATION:CMS\, MR13
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