Advanced Studies in Pure Mathematics

An introduction to $BV$ functions in Wiener spaces

Michele Miranda Jr., Matteo Novaga, and Diego Pallara

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Abstract

We present the foundations of the theory of functions of bounded variation and sets of finite perimeter in abstract Wiener spaces.

Article information

Source
Variational Methods for Evolving Objects, L. Ambrosio, Y. Giga, P. Rybka and Y. Tonegawa, eds. (Tokyo: Mathematical Society of Japan, 2015), 245-294

Dates
Received: 25 December 2012
Revised: 25 March 2013
First available in Project Euclid: 19 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1539916039

Digital Object Identifier
doi:10.2969/aspm/06710245

Mathematical Reviews number (MathSciNet)
MR3587453

Zentralblatt MATH identifier
1362.28016

Subjects
Primary: 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11] 49Q15: Geometric measure and integration theory, integral and normal currents [See also 28A75, 32C30, 58A25, 58C35] 26E15: Calculus of functions on infinite-dimensional spaces [See also 46G05, 58Cxx]
Secondary: 60H07: Stochastic calculus of variations and the Malliavin calculus

Keywords
Wiener space functions of bounded variation Ornstein–Uhlenbeck semigroup

Citation

Miranda Jr., Michele; Novaga, Matteo; Pallara, Diego. An introduction to $BV$ functions in Wiener spaces. Variational Methods for Evolving Objects, 245--294, Mathematical Society of Japan, Tokyo, Japan, 2015. doi:10.2969/aspm/06710245. https://projecteuclid.org/euclid.aspm/1539916039


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