We study maps of bounded variation defined on a metric measure space and valued intoa 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 testplans.
Maps of bounded variation from PI spaces to metric spaces / Brena, C., Nobili, F., Pasqualetto, E.. - In: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE. - ISSN 2036-2145. - (2023). [10.2422/2036-2145.202307_003]
Maps of bounded variation from PI spaces to metric spaces
Nobili, Francesco;
2023
Abstract
We study maps of bounded variation defined on a metric measure space and valued intoa 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 testplans.File in questo prodotto:
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