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SUMMARY:How Rough Local Geometry Makes Treating Singular Equations Even Ha
 rder
DTSTART:20251105T150000
DTEND:20251105T160000
DTSTAMP:20260525T120916Z
UID:0f993f92e5d5d1d2c303ad8df78b3be845018ef145fb8f9075aedce0
CATEGORIES:Conferences - Seminars
DESCRIPTION:HongYi Chen (University of Illinois Chicago)\nWe identify cond
 itions for which a Dirichlet space(a metric measure space with diffusion) 
 admitting a sub-Gaussian heat kernel would be in the Da Prato-Debussche re
 gime of the $Phi^{n+1}$ equation. For this purpose\, we use heat kernel ba
 sed Besov spaces\, where regularity of Schwartz-type distributions is meas
 ured using the small time behavior of the heat kernel. In the process\, we
  show how many nontrivial parts of the solution theory such as constructio
 n of paraproducts and energy estimates are made more difficult by the roug
 hness of the underlying geometry. These difficulties in fact produce a mor
 e restrictive regime than one may first expect by typical scaling heuristi
 cs.
LOCATION:CM  517 https://plan.epfl.ch/?room=%3DCM%201%20517&dim_floor=1&la
 ng=en&dim_lang=en&tree_groups=centres_nevralgiques_grp%2Cmobilite_acces_gr
 p%2Crestauration_et_commerces_grp%2Censeignement%2Cservices_campus_gr
STATUS:CONFIRMED
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