On sets of finite perimeter in Wiener spaces: reduced boundary and convergence to halfspaces

DOI10.4171/RLM/647zbMath1282.28002arXiv1206.6307OpenAlexW2032592174WikidataQ112632004 ScholiaQ112632004MaRDI QIDQ2376638

Eris Runa, Alessio Figalli, Luigi Ambrosio

Publication date: 24 June 2013

Published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.6307

zbMATH Keywords

BV-functionsGaussian perimeterGaussian Banach space

Mathematics Subject Classification ID

Applications of stochastic analysis (to PDEs, etc.) (60H30) Length, area, volume, other geometric measure theory (28A75) 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)

Related Items (5)

Gaussian noise sensitivity and Fourier tails ⋮ Some fine properties of BV functions on Wiener spaces ⋮ Exact periodic stripes for minimizers of a local/nonlocal interaction functional in general dimension ⋮ Lagrangian flows driven by \(BV\) fields in Wiener spaces ⋮ \textit{BV} functions on convex domains in Wiener spaces

Cites Work

• Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces
• Hausdorff measures on the Wiener space.
• Sets of finite perimeter and the Hausdorff-Gauss measure on the Wiener space
• Sets with finite perimeter in Wiener spaces, perimeter measure and boundary rectifiability
• BV functions in abstract Wiener spaces
• BV functions and distorted Ornstein Uhlenbeck processes over the abstract Wiener space
• On semi-martingale characterizations of functionals of symmetric Markov processes
• Su una teoria generale della misura \((r-1)\)-dimensionale in uno spazio ad \(r\) dimensioni
• On the space of BV functions and a related stochastic calculus in infinite dimensions
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