Lagrangian flows driven by $BV$ fields in Wiener spaces

Abstract

We establish the renormalization property for essentially bounded solutions of the continuity equation associated to $BV$ fields in Wiener spaces, with values in the associated Cameron-Martin space; thus obtaining, by standard arguments, new uniqueness and stability results for correspondent Lagrangian $L^{\infty }$-flows. An example related to Neumann elliptic problems is also discussed.

Cited by in corpus (1)

• Well posedness of Lagrangian flows and continuity equations in metric measure spaces