Perimeter of sublevel sets in infinite dimensional spaces-Reference-Cited by-同舟云学术

Perimeter of sublevel sets in infinite dimensional spaces

Published:2012-01 Issue:1 Volume:5 Page:59-76
ISSN:1864-8266
Container-title:Advances in Calculus of Variations
language:en
Short-container-title:

Author:

Caselles Vicent¹,Lunardi Alessandra²,Miranda jr Michele³,Novaga Matteo⁴

Affiliation:

1. Departament de Tecnologies de la Informació i les Comunicacions, Universitat Pompeu–Fabra, C/Roc Boronat 138, 08018 Barcelona, Spain

2. Dipartimento di Matematica, University of Parma, Parco Area delle Scienze 53/a, 43124 Parma, Italy

3. Dipartimento di Matematica, University of Ferrara, via Machiavelli 35, 44121 Ferrara, Italy

4. Dipartimento di Matematica, University of Padova, via Trieste 63, 35121 Padova, Italy

Abstract

Abstract. We compare the perimeter measure with the Airault–Malliavin surface measure and we prove that all open convex subsets of abstract Wiener spaces have finite perimeter. By an explicit counter-example, we show that in general this is not true for compact convex domains.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/acv.2011.010/pdf

Reference13 articles.

1. BV functions in abstract Wiener spaces

2. Sets with finite perimeter in Wiener spaces, perimeter measure and boundary rectifiability

3. Hausdorff measures on the Wiener space

4. BV Functions and Distorted Ornstein Uhlenbeck Processes over the Abstract Wiener Space

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