A DESCRIPTION OF TRANSPORT COST FOR SIGNED MEASURES

摘要

In this paper, we develop the analysis started in a paper by Ambrosio, Mainini, and Serfaty about the extension of the optimal transport framework to the space of real measures. The main motivation comes from the study of nonpositive solutions to some evolution PDEs. Although a canonical optimal transport distance does not seem to be available, we may describe the cost for transporting signed measures in various ways and with interesting properties.