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 13 Aug 2019


Submitted Paper

Inserted: 29 jul 2019
Last Updated: 13 aug 2019

Year: 2019

ArXiv: 1907.11589 PDF


In this paper we characterize the extremal points of the unit ball of a coercive version of the Benamou-Brenier energy proving that they consist of pairs of measures concentrated on absolutely continuous curves. 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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