\(BV\) functions on open domains: the Wiener case and a Fomin differentiable case

DOI10.3934/cpaa.2020117zbMath1441.49036OpenAlexW3010171345MaRDI QIDQ2308265

Giorgio Menegatti, Davide Addona, Michele~jun. Miranda

Publication date: 26 March 2020

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/cpaa.2020117

zbMATH Keywords

functions of bounded variationgeometric measure theoryinfinite-dimensional analysisFomin differentiable measuresopen domains in Wiener spaces

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Stochastic calculus of variations and the Malliavin calculus (60H07) Absolutely continuous real functions of several variables, functions of bounded variation (26B30) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Variational problems in infinite-dimensional spaces (58E99)

Related Items (7)

Surface measures and integration by parts formula on levels sets induced by functionals of the Brownian motion in \(\mathbb{R}^n\) ⋮ Regularity of distributions of Sobolev mappings in abstract settings ⋮ Sobolev and Besov classes on infinite-dimensional spaces ⋮ Characterizations of Sobolev spaces on sublevel sets in abstract Wiener spaces ⋮ On integration by parts formula on open convex sets in Wiener spaces ⋮ On functions of bounded variation on convex domains in Hilbert spaces ⋮ Pointwise conditions for membership of functions in weighted Sobolev classes

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Maximal \(L^2\) regularity for Dirichlet problems in Hilbert spaces
• Partitions of unity in Sobolev spaces over infinite dimensional state spaces
• BV functions in abstract Wiener spaces
• BV functions and distorted Ornstein Uhlenbeck processes over the abstract Wiener space
• Perturbation theory for linear operators.
• \(L ^{2}\)-theory for non-symmetric Ornstein-Uhlenbeck semigroups on domains
• On integration by parts formula on open convex sets in Wiener spaces
• Sobolev functions on infinite-dimensional domains
• Equivalent definitions of \(BV\) space and of total variation on metric measure spaces
• \textit{BV} functions on convex domains in Wiener spaces
• Su una teoria generale della misura \((r-1)\)-dimensionale in uno spazio ad \(r\) dimensioni
• Malliavin calculus for non-Gaussian differentiable measures and surface measures in Hilbert spaces
• Nonsmooth differential geometry– An approach tailored for spaces with Ricci curvature bounded from below
• Sobolev spaces with respect to a weighted Gaussian measure in infinite dimensions
• H = W
• On the Ornstein–Uhlenbeck operator in convex subsets of Banach spaces
• On the space of BV functions and a related stochastic calculus in infinite dimensions

This page was built for publication: \(BV\) functions on open domains: the Wiener case and a Fomin differentiable case