Published Paper

Inserted: 29 jul 2019
Last Updated: 13 jul 2023

Journal: Bulletin of the London Mathematical Society
Year: 2021
Doi: https://doi.org/10.1112/blms.12509

Abstract:

In this paper we characterize the extremal points of the unit ball of the Benamou--Brenier energy and of a coercive generalization of it, both subjected to the homogeneous continuity equation constraint. We prove that extremal points consist of pairs of measures concentrated on absolutely continuous curves which are characteristics of the continuity equation. Then, we apply this result to provide a representation formula for sparse solutions of dynamic inverse problems with finite dimensional data and optimal-transport based regularization.

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