Some Fine Properties of BV Functions on Wiener Spaces

• Autorzy: Luigi Ambrosio , Michele Miranda Jr. , Diego Pallara
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Wiener space; functions of bounded variation

Kategorie tematyczne

• 26E15: Calculus of functions on infinite-dimensional spaces
• 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
• 60H07: Stochastic calculus of variations and the Malliavin calculus

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2015
• Tom: 3
• Numer: 1

Daty

otrzymano

2015-01-10

zaakceptowano

2015-06-09

online

2015-08-14

Twórcy

autor

Luigi Ambrosio

• Scuola Normale Superiore Piazza dei Cavalieri,7, 56126 Pisa, Italy

autor

Michele Miranda Jr.

• Dip. di Matematica e Informatica, Università di Ferrara, via Machiavelli 30, 44121 Ferrara, Italy

autor

Diego Pallara

• Dip. di Matematica e Fisica “Ennio De Giorgi”, Università del Salento, P.O.B. 193, 73100 Lecce, Italy

Bibliografia

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Identyfikatory

DOI

10.1515/agms-2015-0013