On master test plans for the space of BV functions-Reference-Cited by-同舟云学术

On master test plans for the space of BV functions

Published:2022-05-31 Issue:0 Volume:0 Page:
ISSN:1864-8258
Container-title:Advances in Calculus of Variations
language:en
Short-container-title:

Author:

Nobili Francesco¹^ORCID,Pasqualetto Enrico²^ORCID,Schultz Timo³^ORCID

Affiliation:

1. SISSA , Via Bonomea 265, 34136 Trieste , Italy

2. Scuola Normale Superiore , Piazza dei Cavalieri, 7, 56126 Pisa , Italy

3. Fakultät für Mathematik , Universität Bielefeld , Postfach 100131, 33501 Bielefeld ; and Institute for Applied Mathematics, University of Bonn, Endenicher Allee 60, 53115 Bonn , Germany

Abstract

Abstract We prove that on an arbitrary metric measure space a countable collection of test plans is sufficient to recover all BV

{\operatorname{BV}}

functions and their total variation measures. In the setting of non-branching 𝖢𝖣 ⁢ ( K , N )

{\mathsf{CD}(K,N)}

spaces (with finite reference measure), we can additionally require these test plans to be concentrated on geodesics.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/acv-2021-0078/pdf

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