TY - JOUR
T1 - Optimal transport with discrete long-range mean-field interactions
AU - Liu, Jiakun
AU - Loeper, Grégoire
PY - 2020/5/12
Y1 - 2020/5/12
N2 - 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.].
AB - 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.].
KW - Optimal transport
KW - reconstruction problem
KW - time-discrete
UR - http://www.scopus.com/inward/record.url?scp=85086153043&partnerID=8YFLogxK
U2 - 10.1142/S1664360720500113
DO - 10.1142/S1664360720500113
M3 - Article
AN - SCOPUS:85086153043
SN - 1664-3607
JO - Bulletin of Mathematical Science
JF - Bulletin of Mathematical Science
M1 - 2050011
ER -