Some Fine Properties of BV Functions on Wiener 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 cha...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2015-08-01
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| Series: | Analysis and Geometry in Metric Spaces |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/agms-2015-0013 |
| _version_ | 1819131882771578880 |
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| author | Ambrosio Luigi Miranda Jr. Michele Pallara Diego |
| author_facet | Ambrosio Luigi Miranda Jr. Michele Pallara Diego |
| author_sort | Ambrosio Luigi |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-22T09:22:34Z |
| format | Article |
| id | doaj.art-ef7c6d4b200845a9b3cfbcce7af8c3b6 |
| institution | Directory Open Access Journal |
| issn | 2299-3274 |
| language | English |
| last_indexed | 2024-12-22T09:22:34Z |
| publishDate | 2015-08-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Analysis and Geometry in Metric Spaces |
| spelling | doaj.art-ef7c6d4b200845a9b3cfbcce7af8c3b62022-12-21T18:31:10ZengDe GruyterAnalysis and Geometry in Metric Spaces2299-32742015-08-013110.1515/agms-2015-0013agms-2015-0013Some Fine Properties of BV Functions on Wiener SpacesAmbrosio Luigi0Miranda Jr. Michele1Pallara Diego2Scuola Normale Superiore Piazza dei Cavalieri,7, 56126 Pisa, ItalyDip. di Matematica e Informatica, Università di Ferrara, via Machiavelli 30, 44121 Ferrara, ItalyDip. di Matematica e Fisica “Ennio De Giorgi”, Università del Salento, P.O.B. 193, 73100 Lecce, ItalyIn 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.https://doi.org/10.1515/agms-2015-0013wiener spacefunctions of bounded variationprimary: 58e 26e15secondary: 28c20 60h07 |
| spellingShingle | Ambrosio Luigi Miranda Jr. Michele Pallara Diego Some Fine Properties of BV Functions on Wiener Spaces Analysis and Geometry in Metric Spaces wiener space functions of bounded variation primary: 58e 26e15 secondary: 28c20 60h07 |
| title | Some Fine Properties of BV Functions on Wiener Spaces |
| title_full | Some Fine Properties of BV Functions on Wiener Spaces |
| title_fullStr | Some Fine Properties of BV Functions on Wiener Spaces |
| title_full_unstemmed | Some Fine Properties of BV Functions on Wiener Spaces |
| title_short | Some Fine Properties of BV Functions on Wiener Spaces |
| title_sort | some fine properties of bv functions on wiener spaces |
| topic | wiener space functions of bounded variation primary: 58e 26e15 secondary: 28c20 60h07 |
| url | https://doi.org/10.1515/agms-2015-0013 |
| work_keys_str_mv | AT ambrosioluigi somefinepropertiesofbvfunctionsonwienerspaces AT mirandajrmichele somefinepropertiesofbvfunctionsonwienerspaces AT pallaradiego somefinepropertiesofbvfunctionsonwienerspaces |