# A Di Perna-Lions Theory on Wiener Spaces

## Dario Trevisan (Università degli Studi di Pisa, Italy)

created by velichkov on 02 Dec 2013

4 dec 2013 -- 17:00   [open in google calendar]

Aula Seminari - Department of Mathematics, University of Pisa

Abstract.

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 fi elds 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 fi elds in Wiener spaces, ArXiv e-prints (2013).

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