A1 Journal article (refereed)
Multi-marginal entropy-transport with repulsive cost (2020)
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
JYU authors or editors
Publication details
All authors or editors: Gerolin, Augusto; Kausamo, Anna; Rajala, Tapio
Journal or series: Calculus of Variations and Partial Differential Equations
ISSN: 0944-2669
eISSN: 1432-0835
Publication year: 2020
Volume: 59
Issue number: 3
Article number: 90
Publisher: Springer
Publication country: Germany
Publication language: English
DOI: https://doi.org/10.1007/s00526-020-01735-3
Publication open access: Openly available
Publication channel open access: Partially open access channel
Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/68738
Web address of parallel published publication (pre-print): https://arxiv.org/abs/1907.07900
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.
Keywords: partial differential equations; mathematical optimisation
Contributing organizations
Related projects
- Local and global structure of metric measure spaces with Ricci curvature lower bounds
- Rajala, Tapio
- Academy of Finland
- Ricci-kaarevuuden alarajat metrisissä av
- Rajala, Tapio
- Academy of Finland
- Local and global structure of metric measure spaces with Ricci curvature lower bounds (research costs)
- Rajala, Tapio
- Academy of Finland
- Geometric Aspects of Sobolev Space Theory
- Rajala, Tapio
- Academy of Finland
Ministry reporting: Yes
Reporting Year: 2020
JUFO rating: 2