Calculus and fine properties of functions of bounded variation on RCD spaces

We generalize the classical calculus rules satisfied by functions of bounded variation to the framework of RCD spaces. In the infinite dimensional setting we are able to define an analogue of the distributional differential and on finite dimensional spaces we prove fine properties and suitable calcu...

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Bibliographic Details
Published inarXiv.org
Main Authors Brena, Camillo, Gigli, Nicola
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 08.04.2022
Subjects
Calculus
Mathematics - Functional Analysis
Mathematics - Metric Geometry
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Summary:We generalize the classical calculus rules satisfied by functions of bounded variation to the framework of RCD spaces. In the infinite dimensional setting we are able to define an analogue of the distributional differential and on finite dimensional spaces we prove fine properties and suitable calculus rules, such as the Vol'pert chain rule for vector valued functions.
ISSN:2331-8422
DOI:10.48550/arxiv.2204.04174