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Bulletin of Irkutsk State University. Series Mathematics, 2022, Volume 41, Pages 96–106
DOI: https://doi.org/10.26516/1997-7670.2022.41.96 (Mi iigum497) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Integro-differential equations and functional analysis

Nonlinear Kantorovich problems with a parameter

Vladimir I. Bogachevabcd, Ilya I. Malofeevbc

a Lomonosov Moscow State University, Moscow, Russian Federation
b National Research University Higher School of Economics, Moscow, Russian Federation
c Saint Tikhon's Orthodox University, Moscow, Russian Federation
d Moscow Center for Fundamental and Applied Mathematics, Moscow, Russian Federation
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DOI: https://doi.org/10.26516/1997-7670.2022.41.96
Abstract: We consider nonlinear Kantorovich problems with marginal distributions and cost functions depending measurably on a parameter and prove that there exist optimal transportation plans that are also measurable with respect to the parameter. Unlike the classical linear Kantorovich problem of minimization of the integrals of a given cost function with respect to transportation plans, we deal with nonlinear cost functionals in which integrands depend on transportation plans. Dependence of cost functions on conditional measures of transportation plans is also allowed.
Keywords: Kantorovich problem, optimal plan, measurability with respect to a parameter.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00432
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-284
Russian Science Foundation 19-71-3002
Foundation for the Development of Science, Education and Family "Living Tradition"
This research is supported by the Saint Tiknon’s Orthodox University, the Foundation “Living tradition” and the Russian Foundation for Basic Research Grant 20-01-00432. The results of Section 2 (Theorem 1) have been supported by the Ministry of Education and Science of the Russian Federation as part of the program of the Moscow Center for Fundamental and Applied Mathematics under the agreement N 075-15-2022-284. The results of Section 3 (Theorem 2) have been supported by the RSF grant N 19-71-30020.
Received: 17.03.2022
Revised: 12.07.2022
Accepted: 19.07.2022
Document Type: Article
UDC: 517.9
MSC: 49Q22, 28C15, 28A33, 46E27
Language: English
Citation: Vladimir I. Bogachev, Ilya I. Malofeev, “Nonlinear Kantorovich problems with a parameter”, Bulletin of Irkutsk State University. Series Mathematics, 41 (2022), 96–106
Citation in format AMSBIB
\Bibitem{BogMal22}
\by Vladimir~I.~Bogachev, Ilya~I.~Malofeev
\paper Nonlinear Kantorovich problems with a parameter
\jour Bulletin of Irkutsk State University. Series Mathematics
\yr 2022
\vol 41
\pages 96--106
\mathnet{http://mi.mathnet.ru/iigum497}
\crossref{https://doi.org/10.26516/1997-7670.2022.41.96}
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