Calculus of Variations and Geometric Measure Theory

A. Gerolin - A. Kausamo - T. Rajala

Multi-marginal Entropy-Transport with repulsive cost

created by gerolin on 19 Jul 2019
modified on 31 May 2020


Published Paper

Inserted: 19 jul 2019
Last Updated: 31 may 2020

Journal: Calculus of Variations and Partial Differential Equations
Volume: 59
Number: 90
Year: 2020

ArXiv: 1907.07900 PDF


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 also prove the entropy-regularized version of the Kantorovich duality.