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Funktsional'nyi Analiz i ego Prilozheniya, 2024, Volume 58, Issue 2, Pages 137–156
DOI: https://doi.org/10.4213/faa4106 (Mi faa4106) 		 
Continuous selection of approximate Monge solutions in the Kantorovich problem with a parameter

Svetlana Popovaabc

a Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region, Russia
b NRU Higher School of Economics, Moscow, Russia
c Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow, Russia
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DOI: https://doi.org/10.4213/faa4106
Abstract: We consider the Kantorovich optimal transportation problem in the case where the cost function and marginal distributions continuously depend on a parameter with values in a metric space. We prove the existence of approximate optimal Monge mappings continuous with respect to the parameter.
Keywords: Kantorovich problem, Monge problem, optimal transportation problem, continuity with respect to a parameter.
Funding agency Grant number
Russian Science Foundation 22-11-00015
Received: 10.03.2023
Revised: 06.07.2023
Accepted: 22.07.2023
English version:
Functional Analysis and Its Applications, 2024, Volume 58, Issue 2, Pages 212–227
DOI: https://doi.org/10.1134/S0016266324020096
Bibliographic databases:
Document Type: Article
MSC: 49Q22, 60B10
Language: Russian
Citation: Svetlana Popova, “Continuous selection of approximate Monge solutions in the Kantorovich problem with a parameter”, Funktsional. Anal. i Prilozhen., 58:2 (2024), 137–156; Funct. Anal. Appl., 58:2 (2024), 212–227
Citation in format AMSBIB
\Bibitem{Pop24}
\by Svetlana~Popova
\paper Continuous selection of approximate Monge solutions in the Kantorovich problem with a parameter
\jour Funktsional. Anal. i Prilozhen.
\yr 2024
\vol 58
\issue 2
\pages 137--156
\mathnet{http://mi.mathnet.ru/faa4106}
\crossref{https://doi.org/10.4213/faa4106}
\transl
\jour Funct. Anal. Appl.
\yr 2024
\vol 58
\issue 2
\pages 212--227
\crossref{https://doi.org/10.1134/S0016266324020096}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85199169496}
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    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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