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SUMMARY:OPTIMAL REGULARITY FOR SUPERCRITICAL PARABOLIC OBSTACLE PROBLEMS
DTSTART:20220513T141500
DTSTAMP:20260505T053955Z
UID:52aacf9d7a9c7ec44c0c923ae12211ead618de4f93ee30401a7ab4df
CATEGORIES:Conferences - Seminars
DESCRIPTION:Damià Torres-Latorre\, Univ. Barcelona\nAbstract. The nonloca
 l parabolic obstacle problem for an elliptic operator L with zero obstacle
  is\n\n\nWhen L is the Laplacian\, this problem is closely related to the 
 Stefan problem\, that models phase transitions. When L is a nonlocal opera
 tor such as the fractional laplacian (−∆)s\, the equation serves as a 
 model for stock pricing and other random processes with jumps.\nThe ellipt
 ic (time-stationary) version of this problem has been thoroughly studied s
 ince the pioneer works of Caffarelli\, Salsa and Silvestre around 2007. Ho
 wever\, much less is known about the parabolic problem.\nWhen L is the fra
 ctional Laplacian\, Caffarelli and Figalli proved in 2013 that the solutio
 ns are C1\,s in space and C1\,α in time. Still in the case of (−∆)s\,
  for s  > 1/2\, Barrios\, Figalli and Ros-Oton proved that the free bound
 ary is C1\,α at regular points.\nIn this talk\, we present our recent res
 ults with X. Ros-Oton\, where we proved the optimal regularity of the solu
 tions and a global C1\,α free boundary regularity\nfor the case s < 1/2 .
LOCATION:GC A1 416 https://plan.epfl.ch/?room==GC%20A1%20416
STATUS:CONFIRMED
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