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arXiv · 1809.07432

Optimal transport with discrete long range mean field interactions

Jiakun Liu·Grégoire Loeper
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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.

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Jiakun Liu, Grégoire Loeper. 2018-09-19. Optimal transport with discrete long range mean field interactions. https://arxiv.org/abs/1809.07432

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