Multi-marginal entropy-transport with repulsive cost
Gerolin, Augusto; Kausamo, Anna; Rajala, Tapio (2020). Multi-marginal entropy-transport with repulsive cost. Calculus of Variations and Partial Differential Equations, 59 (3), 90. DOI: 10.1007/s00526-020-01735-3
© The Authors 2020
In this paper we study theoretical properties of the entropy-transport functional with repulsive cost functions. We provide sufficient conditions for the existence of a minimizer in a class of metric spaces and prove the Γ-convergence of the entropy-transport functional to a multi-marginal optimal transport problem with a repulsive cost. We point out that our construction can deal with the case when the space X is a domain in Rd, answering a question raised in Benamou et al. (Numer Math 142:33–54, 2019). Finally, we also prove the entropy-regularized version of the Kantorovich duality.