RIS ID
143727
Abstract
2020 The Author(s). The Author(s). 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.].
Grant Number
ARC/DP200101084, ARC/DP170100929
Publication Details
Liu, J. & Loeper, G. (2020). Optimal transport with discrete long-range mean-field interactions. Bulletin of Mathematical Sciences, 2050011-1-2050011-26.