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.
CITATION STYLE
Liu, J., & Loeper, G. (2019). Optimal Transport with Discrete Mean Field Interaction (pp. 207–212). https://doi.org/10.1007/978-3-030-04161-8_15
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