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arXiv · 2306.00768

Maps of bounded variation from PI spaces to metric spaces

Camillo Brena·Francesco Nobili·Enrico Pasqualetto
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Abstract

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.

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Camillo Brena, Francesco Nobili, Enrico Pasqualetto. 2023-06-01. Maps of bounded variation from PI spaces to metric spaces. https://arxiv.org/abs/2306.00768

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