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On flows associated to Sobolev vector fields in Wiener spaces: An approach à la DiPerna-Lions |
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| Authors: | Luigi Ambrosio Alessio Figalli |
| Affiliation: | a Scuola Normale Superiore, Department of Mathematics, Piazza dei Cavalieri 7, Pisa, PI, Italy b Université de Nice Sophia-Antipolis, Laboratoire J.-A. Dieudonné, CNRS UMR 6621, Parc Valrose, 06108 Nice Cedex 02, France |
| Abstract: | In this paper we extend the DiPerna-Lions theory of flows associated to Sobolev vector fields to the case of Cameron-Martin-valued vector fields in Wiener spaces E having a Sobolev regularity. The proof is based on the analysis of the continuity equation in E, and on uniform (Gaussian) commutator estimates in finite-dimensional spaces. |
| Keywords: | Flows Sobolev spaces Wiener spaces |
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