Submitted Paper

Inserted: 20 jun 2025
Last Updated: 20 jun 2025

Year: 2025

Abstract:

In this paper we revisit a class of optimal transport problems associated to non-autonomous linear control systems. Building on properties of the cost functions on $\mathbb{R}^d\times\mathbb{R}^d$ derived from suitable variational problems, we show the equivalence between the static and dynamic versions of the corresponding transport problems. Our analysis is constructive in nature and relies on functional analytic properties of the end-point map and the fine properties of the optimal control functions. These lead to some new quantitative estimates which play a crucial role in our investigation.