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CATEGORIES:Special DPMMS Colloquium
SUMMARY:Recent applications of the DiPerna-Lions theory -
Alessio Figalli\, Austin
DTSTART;TZID=Europe/London:20141002T150000
DTEND;TZID=Europe/London:20141002T160000
UID:TALK54454AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/54454
DESCRIPTION:At the beginning of the 1990?s\, DiPerna and Lions
studied the connection between transport equation
s and ordinary differential equations in detail. I
n particular\, by proving existence and uniqueness
at the level of the transport equation\, they obt
ained (roughly speaking) existence and uniqueness
of solutions for ODEs with Sobolev vector-fields f
or a.e. initial condition. Ten years later\, Ambro
sio has been able to extend this result to BV vect
or fields. In recent years\, several new extension
s have been obtained\, that give rise to applicati
ons to PDEs which include the linear Schrodinger e
quation and the Vlasov-Poisson equation. The aim o
f this talk is to give an introductory overview of
these results.\n
LOCATION:CMS\, MR13
CONTACT:Andrew Aitchison
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