Maps of bounded variation from PI spaces to metric spaces
Functional Analysis
2025-08-05 v2 Analysis of PDEs
Metric Geometry
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.
Cite
@article{arxiv.2306.00768,
title = {Maps of bounded variation from PI spaces to metric spaces},
author = {Camillo Brena and Francesco Nobili and Enrico Pasqualetto},
journal= {arXiv preprint arXiv:2306.00768},
year = {2025}
}
Comments
38 pages. Revised version, to appear in Ann. Sc. norm. super. Pisa - Cl. sci