JournalsaihpcVol. 37, No. 2pp. 343–372

On the existence of dual solutions for Lorentzian cost functions

  • Martin Kell

    Fachbereich Mathematik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany

  • Stefan Suhr

    Ruhr-Universität Bochum, Fakultät für Mathematik, Gebäude NA 4/33, D-44801 Bochum, Germany
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Abstract

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.

Cite this article

Martin Kell, Stefan Suhr, On the existence of dual solutions for Lorentzian cost functions. Ann. Inst. H. Poincaré Anal. Non Linéaire 37 (2020), no. 2, pp. 343–372

DOI 10.1016/J.ANIHPC.2019.09.005