@article{e97410f30bef43abb07082f04bb80ff2,

title = "On the extremal points of the ball of the Benamou–Brenier energy",

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.",

keywords = "35F05 (primary), 49J45, 49N45, 52A05",

author = "Kristian Bredies and Marcello Carioni and Silvio Fanzon and Francisco Romero",

note = "Funding Information: We thank the referee for the useful suggestions provided, particularly for encouraging us to include the case α=0 in the characterization of Theorem 6, which was previously missing. The Institute of Mathematics and Scientific Computing, to which KB, SF and FR are affiliated, is a member of NAWI Graz (http://www.nawigraz.at/en/). The authors KB, SF and FR are further members of/associated with BioTechMed Graz (https://biotechmedgraz.at/en/). Publisher Copyright: {\textcopyright} 2021 The Authors. Bulletin of the London Mathematical Society is copyright {\textcopyright} London Mathematical Society.",

year = "2021",

month = oct,

doi = "10.1112/blms.12509",

language = "English",

volume = "53",

pages = "1436--1452",

journal = "Bulletin of the London Mathematical Society",

issn = "0024-6093",

publisher = "Oxford University Press",

number = "5",

}