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arXiv:2306.00768 [math.FA]AbstractReferencesReviewsResources

Maps of bounded variation from PI spaces to metric spaces

Camillo Brena, Francesco Nobili, Enrico Pasqualetto

Published 2023-06-01Version 1

We study maps of bounded variation defined on a metric measure space and valued into a metric space. Assuming the source space to satisfy a doubling and Poincar\'e property, we produce a well-behaved relaxation theory via approximation by simple maps. Moreover, several equivalent characterizations are given, including a notion in weak duality with test plans.

Comments: 38 pages
Categories: math.FA, math.AP, math.MG
Subjects: 53C23, 26A45, 26B30, 49J52, 30L99
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