A Di Perna-Lions Theory on Wiener Spaces

   In [DL89], R.J. DiPerna and P.-L. Lions first proved that Sobolev regularity for vector fields in $\mathbb{R}^n$ (with bounded divergence) is sufficient to establish existence, uniqueness and stability of a generalized notion of flow, consisting of a suitable selection among the trajectories of the associated ODE: later on, the important case of BV fields was settled by L. Ambrosio, in [Amb04].   In this seminar we will introduce and motivate the infinite dimensional counterparts of these results, in the setting of abstract Wiener spaces, as developed in [AF09] (Sobolev fields) and in [Tre13] (BV fields).
REFERENCES:
[AF09] L. Ambrosio and A. Figalli, On flows associated to Sobolev vector fields in Wiener spaces: an approach a la DiPerna-Lions, J. Funct. Anal. 256 (1) (2009).
[Amb04] L. Ambrosio, Transport equation and Cauchy problem for BV vector elds, Invent. Math. 158 (2) (2004).
[DL89] R. J. DiPerna and P.-L. Lions, Ordinary di erential equations, transport theory and Sobolev spaces, Invent. Math.98 (3) (1989).
[Tre13] D. Trevisan, Lagrangian flows driven by BV fields in Wiener spaces, ArXiv e-prints (2013).
http://cvgmt.sns.it/seminar/329/
            

When	Wed Dec 4, 2013 4pm – 5pm Coordinated Universal Time
Where	Aula Seminari - Department of Mathematics, University of Pisa (map)