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SUMMARY:Regularity Theory of Kinetic Equations with Rough Coefficients
DTSTART:20250326T130000Z
DTEND:20250326T150000Z
DTSTAMP:20260507T130100Z
UID:indico-event-13576@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr
DESCRIPTION:Speakers: Clément Mouhot (University of Cambridge & IHES)\n\n
 The theory of De Giorgi (1958) and Nash (1959) solved Hilbert's 19th prob
 lem and was a major contribution to 20th century PDE analysis. It is conce
 rned with the Hölder regularity of solutions to elliptic and parabolic PD
 Es with rough (merely measurable) coefficients\; it was developed by Moser
  (1960-1964) to include the Harnack inequality. These lectures  are an in
 troduction to a recent active research area (Pascucci-Polidoro\, Wang-Zhan
 g\, Golse-Imbert-M-Vasseur\, Imbert-Silvestre\, Imbert-Guerand\, Guerand-M
 \, Anceschi-Rebucci\, Loher\, Niebel-Zacher...): the extension of this the
 ory to the hypoelliptic PDEs\, local and nonlocal\, that appear naturally 
 in kinetic theory. The simpler prototypical case is the Kolmogorov equatio
 n (aka kinetic Fokker-Planck equation) with a rough matrix of coefficients
  in the kinetic diffusion. The course will in particular emphasize the rec
 ent quantitative robust methods based on the construction of trajectories 
 and their connexions to control theory and hypocoercivity (works with Diet
 er\, Hérau\, Hutridurga\, Niebel\, Zacher).\n\nhttps://indico.math.cnrs.f
 r/event/13576/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/13576/
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