On the existence of dual solutions for Lorentzian cost functions

Kell, Martin; Suhr, Stefan

doi:10.1016/j.anihpc.2019.09.005

Kell, Martin ¹ ; Suhr, Stefan ²

¹ Fachbereich Mathematik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
² Ruhr-Universität Bochum, Fakultät für Mathematik, Gebäude NA 4/33, D-44801 Bochum, Germany

Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 2, pp. 343-372.

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Résumé

The dual problem of optimal transportation in Lorentz-Finsler geometry is studied. It is shown that in general no solution exists even in the presence of an optimal coupling. Under natural assumptions dual solutions are established. It is further shown that the existence of a dual solution implies that the optimal transport is timelike on a set of full measure. In the second part the persistence of absolute continuity along an optimal transportation under obvious assumptions is proven and a solution to the relativistic Monge problem is provided.

MR Zbl

DOI : 10.1016/j.anihpc.2019.09.005

Mots-clés : Optimal transport, Lorentz cost, Dual solution, Relativistic Monge problem

Affiliations des auteurs :

Kell, Martin ¹ ; Suhr, Stefan ²

¹ Fachbereich Mathematik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
² Ruhr-Universität Bochum, Fakultät für Mathematik, Gebäude NA 4/33, D-44801 Bochum, Germany

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     title = {On the existence of dual solutions for {Lorentzian} cost functions},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {343--372},
     publisher = {Elsevier},
     volume = {37},
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     year = {2020},
     doi = {10.1016/j.anihpc.2019.09.005},
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     zbl = {1439.49060},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2019.09.005/}
}

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Kell, Martin; Suhr, Stefan. On the existence of dual solutions for Lorentzian cost functions. Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 2, pp. 343-372. doi : 10.1016/j.anihpc.2019.09.005. http://www.numdam.org/articles/10.1016/j.anihpc.2019.09.005/

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