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SUMMARY:Schauder estimates for degenerate non-local parabolic equations - 
 Lorenzo Marino (Polish Academy of Sciences)
DTSTART:20220224T143000Z
DTEND:20220224T150000Z
UID:TALK167804@talks.cam.ac.uk
DESCRIPTION:In the present talk\, I briefly explain the main analytical re
 sults of my PhD thesis: "Weak regularisation by degenerate L&eacute\;vy no
 ise and its applications". In particular\, I will show the Schauder estima
 tes\, a useful analytical tool for the well-posedness of SDEs\, for two di
 fferent classes of integro-differential equations whose coefficients lie i
 n suitable anisotropic H&ouml\;lder spaces with multi-indices of regularit
 y. The first result focuses on parabolic operators with non-linear drift\,
  when the main part is an &alpha\;-stable operator acting only on the firs
 t component. To deal with the non-linear drift\, some new controls on Beso
 v norms are also presented. As an extension of the first one\, I will then
  show the Schauder estimates for degenerate Ornstein-Uhlenbeck operators d
 riven by a larger class of possibly asymmetric stable-like operators\, suc
 h as the relativistic\, layered or Lamperti stable ones.
LOCATION:Seminar Room 1\, Newton Institute
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