Some Fine Properties of BV Functions on Wiener Spaces

Luigi Ambrosio, Michele Miranda Jr., Diego Pallara
2015 Analysis and Geometry in Metric Spaces  
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.
doi:10.1515/agms-2015-0013 fatcat:fzunspro2vbvhjcqasvf27oe6a