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Analysis and Geometry in Metric Spaces

Ed. by Ritoré, Manuel


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Some Fine Properties of BV Functions on Wiener Spaces

Luigi Ambrosio / Michele Miranda Jr.
  • Corresponding author
  • Dip. di Matematica e Informatica, Università di Ferrara, via Machiavelli 30, 44121 Ferrara, Italy
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Diego Pallara
  • Corresponding author
  • Dip. di Matematica e Fisica “Ennio De Giorgi”, Università del Salento, P.O.B. 193, 73100 Lecce, Italy
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-08-14 | DOI: https://doi.org/10.1515/agms-2015-0013

Abstract

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.

Keywords: Wiener space; functions of bounded variation

MSC: Primary: 58E; 26E15; Secondary: 28C20; 60H07

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About the article

Received: 2015-01-10

Accepted: 2015-06-09

Published Online: 2015-08-14


Citation Information: Analysis and Geometry in Metric Spaces, Volume 3, Issue 1, ISSN (Online) 2299-3274, DOI: https://doi.org/10.1515/agms-2015-0013.

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© 2015 Luigi Ambrosio et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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