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Optimal transport with discrete long-range mean-field interactions

Journal Article


Abstract


  • We study an optimal transport problem where, at some intermediate time, the mass is either accelerated by an external force field or self-interacting. We obtain the regularity of the velocity potential, intermediate density, and optimal transport map, under the conditions on the interaction potential that are related to the so-called Ma-Trudinger-Wang condition from optimal transport [X.-N. Ma, N. S. Trudinger and X.-J. Wang, Regularity of potential functions of the optimal transportation problems, Arch. Ration. Mech. Anal. 177 (2005) 151-183.].

Publication Date


  • 2020

Citation


  • Liu, J., & Loeper, G. (2020). Optimal transport with discrete long-range mean-field interactions. Bulletin of Mathematical Sciences, 10(2). doi:10.1142/S1664360720500113

Scopus Eid


  • 2-s2.0-85086153043

Volume


  • 10

Issue


  • 2

Place Of Publication


Abstract


  • We study an optimal transport problem where, at some intermediate time, the mass is either accelerated by an external force field or self-interacting. We obtain the regularity of the velocity potential, intermediate density, and optimal transport map, under the conditions on the interaction potential that are related to the so-called Ma-Trudinger-Wang condition from optimal transport [X.-N. Ma, N. S. Trudinger and X.-J. Wang, Regularity of potential functions of the optimal transportation problems, Arch. Ration. Mech. Anal. 177 (2005) 151-183.].

Publication Date


  • 2020

Citation


  • Liu, J., & Loeper, G. (2020). Optimal transport with discrete long-range mean-field interactions. Bulletin of Mathematical Sciences, 10(2). doi:10.1142/S1664360720500113

Scopus Eid


  • 2-s2.0-85086153043

Volume


  • 10

Issue


  • 2

Place Of Publication