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BEGIN:VEVENT
UID:news482@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20181229T165147
DTSTART;TZID=Europe/Zurich:20140326T151500
SUMMARY:Seminar Analysis: Dario Trevisan (Scuola Normale Superiore\, Pisa\,
  Italy)
DESCRIPTION:Following [1]\, in this talk we show how to establish\, in a ra
 ther general setting\, an analogue of DiPerna-Lions theory on well-posedne
 ss of flows of ODE’s associated to Sobolev vector fields. Key results ar
 e a well-posedness result for the continuity equation associated to suitab
 ly defined Sobolev vector fields\, via a commutator estimate\, and an abst
 ract superposition principle in (possibly extended) metric measure spaces\
 , via an embedding into R∞.\\r\\nWhen specialized to the setting of Eucl
 idean or infinite dimensional (e.g.Gaussian) spaces\, large parts of previ
 ously known results are recovered at once.Moreover\, the class of RCD(K\,
 ∞) metric measure spaces\, recently introduced by Ambrosio\, Gigli and S
 avar ́e\, object of extensive recent research\, fits into our framework. 
 Therefore we provide\, for the first time\, well-posedness results forODE
 ’s under low regularity assumptions on the velocity and in a non smooth 
 context.\\r\\nReferences:[1] L. Ambrosio and D. Trevisan. Well posedness o
 f Lagrangian flows and continuity equations in metric measure spaces. ArXi
 v e-prints\, February 2014.
X-ALT-DESC: \nFollowing [1]\, in this talk we show how to establish\, in a 
 rather general setting\, an analogue of DiPerna-Lions theory on well-posed
 ness of flows of ODE’s associated to Sobolev vector fields. Key results 
 are a well-posedness result for the continuity equation associated to suit
 ably defined Sobolev vector fields\, via a commutator estimate\, and an ab
 stract superposition principle in (possibly extended) metric measure space
 s\, via an embedding into <b>R</b><sup>∞</sup>.\nWhen specialized to the
  setting of Euclidean or infinite dimensional (e.g.Gaussian) spaces\, larg
 e parts of previously known results are recovered at once.Moreover\, the c
 lass of RCD(K\,∞) metric measure spaces\, recently introduced by Ambrosi
 o\, Gigli and Savar ́e\, object of extensive recent research\, fits into 
 our framework. Therefore we provide\, for the first time\, well-posedness 
 results forODE’s under low regularity assumptions on the velocity and in
  a non smooth context.\n<b>References</b>:<br />[1] L. Ambrosio and D. Tre
 visan. Well posedness of Lagrangian flows and continuity equations in metr
 ic measure spaces. ArXiv e-prints\, February 2014.
DTEND;TZID=Europe/Zurich:20140326T161500
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