Optimal transport with discrete long range mean field interactions
Analysis of PDEs
2018-09-21 v1 Mathematical Physics
math.MP
Abstract
We study an optimal transport problem where, at some intermediate time, the mass is accelerated by either an external force field, or self-interacting. We obtain regularity of the velocity potential, intermediate density, and optimal transport map, under conditions on the interaction potential that are related to the so-called Ma-Trudinger-Wang condition from optimal transport.
Keywords
Cite
@article{arxiv.1809.07432,
title = {Optimal transport with discrete long range mean field interactions},
author = {Jiakun Liu and Grégoire Loeper},
journal= {arXiv preprint arXiv:1809.07432},
year = {2018}
}