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.
@article{bwmeta1.element.doi-10_1515_agms-2015-0013,
author = {Luigi Ambrosio and Michele Miranda Jr. and Diego Pallara},
title = {Some Fine Properties of BV Functions on Wiener Spaces},
journal = {Analysis and Geometry in Metric Spaces},
volume = {3},
year = {2015},
zbl = {1321.26058},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_agms-2015-0013}
}
Luigi Ambrosio; Michele Miranda Jr.; Diego Pallara. Some Fine Properties of BV Functions on Wiener Spaces. Analysis and Geometry in Metric Spaces, Tome 3 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_agms-2015-0013/
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