Calculus of Variations and Geometric Measure Theory

L. Ambrosio - A. Figalli

On flows associated to Sobolev vector fields in Wiener spaces: an approach a' la DiPerna-Lions

created by ambrosio on 10 Mar 2008
modified by figalli on 04 Jun 2008


Accepted Paper

Inserted: 10 mar 2008
Last Updated: 4 jun 2008

Journal: J. Funct. Anal.
Year: 2008


In this paper we extend the DiPerna-Lions theory of flows associated to Sobolev vector fields to an infinite-dimensional setup. More precisely, we consider Cameron-Martin valued vector fields in Wiener spaces having a Sobolev regularity with respect to the spatial variables, and prove (under suitable integrability assumptions on the Gaussian divergence) existence, uniqueness and stability of the flow. The proof uses a delicate finite-dimensional commutator argument, with estimates independent of the dimension.

Keywords: Wiener spaces, Sobolev spaces, Flows