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Some Fine Properties of BV Functions on Wiener Spaces

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In this paper we define jump set and approximate limits for BV functions on Wiener spaces and show that the weak gradient admits a decomposition similar to the finite dimensional case. We also define the SBV class of functions of special bounded variation and give a characterisation of SBV via a chain rule and a closure theorem. We also provide a characterisation of BV functions in terms of the short-time behaviour of the Ornstein-Uhlenbeck semigroup following an approach due to Ledoux.

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  • Scuola Normale Superiore Piazza dei Cavalieri,7, 56126 Pisa, Italy
  • Dip. di Matematica e Informatica, Università di Ferrara, via Machiavelli 30, 44121 Ferrara, Italy
  • Dip. di Matematica e Fisica “Ennio De Giorgi”, Università del Salento, P.O.B. 193, 73100 Lecce, Italy


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