In this paper we provide the first extension of the DiPerna–Lions theory of flows associated to Sobolev vector fields to infinite-dimensional spaces, in particular to Cameron–Martin-valued vector fields defined in Wiener spaces E and 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.
On flows associated to Sobolev vector fields in Wiener spaces: an approach a la DiPerna-Lions
AMBROSIO, Luigi;
2009
Abstract
In this paper we provide the first extension of the DiPerna–Lions theory of flows associated to Sobolev vector fields to infinite-dimensional spaces, in particular to Cameron–Martin-valued vector fields defined in Wiener spaces E and 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.File in questo prodotto:
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