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SUMMARY:Minimising a relaxed Willmore functional for graphs subject to Dir
 ichlet boundary conditions - Deckelnick\, K 
DTSTART:20150910T100000Z
DTEND:20150910T113000Z
UID:TALK60646@talks.cam.ac.uk
CONTACT:42080
DESCRIPTION:For a bounded smooth domain $Omega$ in the plane we consider t
 he minimisation of the Willmore functional for graphs subject to Dirichlet
  boundary conditions. In a first step we show that sequences of functions 
 with bounded Willmore energy satisfy uniform area and diameter bounds yiel
 ding compactness in $L^1(Omega)$. We therefore introduce the $L^1$--lower 
 semicontinuous relaxation and prove that it coincides with the Willmore fu
 nctional on the subset of $H^2(Omega)$ satisfying the given Dirichlet boun
 dary conditions. Furthermore\, we derive properties of functions having fi
 nite relaxed Willmore energy with special emphasis on the attainment of th
 e boundary conditions. Finally we show that the relaxed Willmore functiona
 l has a minimum in $L^{infty}(Omega) 
p BV(Omega)$. This is joint work wit
 h Hans--Christoph Grunau (Magdeburg) and Matthias Rger (Dortmund).\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
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