Multi-marginal entropy-transport with repulsive cost
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.
Main Authors
Format
Articles
Research article
Published
2020
Series
Subjects
Publication in research information system
Publisher
Springer
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202004282942Käytä tätä linkitykseen.
Review status
Peer reviewed
ISSN
0944-2669
DOI
https://doi.org/10.1007/s00526-020-01735-3
Language
English
Published in
Calculus of Variations and Partial Differential Equations
Citation
- Gerolin, A., Kausamo, A., & Rajala, T. (2020). Multi-marginal entropy-transport with repulsive cost. Calculus of Variations and Partial Differential Equations, 59(3), Article 90. https://doi.org/10.1007/s00526-020-01735-3
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Funder(s)
Research Council of Finland
Research Council of Finland
Research Council of Finland
Research Council of Finland
Funding program(s)
Research costs of Academy Research Fellow, AoF
Research costs of Academy Research Fellow, AoF
Academy Research Fellow, AoF
Academy Project, AoF
Akatemiatutkijan tutkimuskulut, SA
Akatemiatutkijan tutkimuskulut, SA
Akatemiatutkija, SA
Akatemiahanke, SA
Additional information about 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.
Copyright© The Authors 2020