Maps of bounded variation from PI spaces to metric spaces

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 Poincaré 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.

38 pages. Revised version, to appear in Ann. Sc. norm. super. Pisa - Cl. sci