Calculus of Variations and Geometric Measure Theory
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K. Bredies - M. Carioni - S. Fanzon - F. Romero

On the extremal points of the ball of the Benamou-Brenier energy

created by carioni on 29 Jul 2019
modified by fanzon on 14 May 2021


Published Paper

Inserted: 29 jul 2019
Last Updated: 14 may 2021

Journal: Bulletin of the London Mathematical Society
Year: 2021

ArXiv: 1907.11589 PDF


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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