Maps of bounded variation from PI spaces to metric spaces (2306.00768v1)

Published 1 Jun 2023 in math.FA, math.AP, and math.MG

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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