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SUMMARY:Flatness implies smoothness for the porous medium equation - Koch\
 , H (University of Bonn)
DTSTART:20140212T140000Z
DTEND:20140212T150000Z
UID:TALK50820@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We call a solution to the porous medium equation flat on a uni
 t size space time cylinder if it is sandwiched between two close and paral
 lel traveling wave solutions of velocity 1.  \nThose solutions are smooth 
 in the sense that the pressure is a smooth function on the closure of its 
 support\, and inside a smaller space time cylinder\, with nonvanishing gra
 dient at the boundary of the support. The proof follows  Caffarellis strat
 egy of improving the flatness for rescaled solutions. An important part co
 nsists in a linearization of equation and geometry.  \n\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
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