Abstract
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.
| Original language | English |
|---|---|
| Article number | 90 |
| Pages (from-to) | 1-20 |
| Number of pages | 20 |
| Journal | Calculus of Variations and Partial Differential Equations |
| Volume | 59 |
| Issue number | 3 |
| Early online date | 23 Apr 2020 |
| DOIs | |
| Publication status | Published - 1 Jun 2020 |
Funding
The authors acknowledge the support of the Academy of Finland, Projects Nos. 274372, 284511, 312488, and 314789. A.G. also acknowledges funding by the European Research Council under H2020/MSCA-IF “OTmeetsDFT” (Grant ID: 795942). A.K. also wants to thank the Vilho, Yrjö and Kalle Väisälä Foundation for funding.
| Funders | Funder number |
|---|---|
| Vilho, Yrjö and Kalle Väisälä Foundation | |
| Horizon 2020 Framework Programme | 795942 |
| European Research Council | |
| Vrije Universiteit Amsterdam | |
| Academy of Finland | 314789, 312488, 284511, 274372 |