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

Kausamo, Anna
Rajala, Tapio

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

Fields of science: