Multi-marginal entropy-transport with repulsive cost
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
Date
2020Discipline
MatematiikkaAnalyysin ja dynamiikan tutkimuksen huippuyksikköMathematicsAnalysis and Dynamics Research (Centre of Excellence)Copyright
© The Authors 2020
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.
Publisher
SpringerISSN Search the Publication Forum
0944-2669Publication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/35298830
Metadata
Show full item recordCollections
Related funder(s)
Research Council of FinlandFunding program(s)
Research costs of Academy Research Fellow, AoF; Academy Research Fellow, AoF; Academy Project, AoFAdditional 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.License
Related items
Showing items with similar title or keywords.
-
On deterministic solutions for multi-marginal optimal transport with Coulomb cost
Bindini, Ugo; De Pascale, Luigi; Kausamo, Anna (American Institute of Mathematical Sciences (AIMS), 2022)In this paper we study the three-marginal optimal mass transportation problem for the Coulomb cost on the plane R2. The key question is the optimality of the so-called Seidl map, first disproved by Colombo and Stra. We ... -
On the Structure of Multi-marginal Optimal Mass Transportation in Metric Spaces
Kausamo, Anna (Jyväskylän yliopisto, 2019) -
Shape optimization utilizing consistent sensitivities
Toivanen, Jukka (University of Jyväskylä, 2010) -
On optimal shape design of systems governed by mixed Dirichlet-Signorini boundary value problems
Haslinger, J.; Neittaanmäki, Pekka (University of Jyväskylä, 1983)