Abstract:
We discuss Kantorovich problems with a parameter and density constraints. Also we give some new results on the continuity of solutions with respect to a parameter along with a survey of results on measurability of solutions with respect to a parameter.
Keywords:
Kantorovich problem, Kantorovich problem with a density constraint, continuity with respect to a parameter, measurability with respect to a parameter.
This paper was supported by the Russian Foundation for Basic Research (Grant no. 20–01–00432)
and the Moscow Center of Fundamental and Applied Mathematics.
Citation:
V. I. Bogachev, “Kantorovich problems with a parameter and density constraints”, Sibirsk. Mat. Zh., 63:1 (2022), 42–57; Siberian Math. J., 63:1 (2022), 34–47
\Bibitem{Bog22}
\by V.~I.~Bogachev
\paper Kantorovich problems with a~parameter and density constraints
\jour Sibirsk. Mat. Zh.
\yr 2022
\vol 63
\issue 1
\pages 42--57
\mathnet{http://mi.mathnet.ru/smj7640}
\crossref{https://doi.org/10.33048/smzh.2022.63.103}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4440264}
\transl
\jour Siberian Math. J.
\yr 2022
\vol 63
\issue 1
\pages 34--47
\crossref{https://doi.org/10.1134/S0037446622010037}
Linking options:
https://www.mathnet.ru/eng/smj7640
https://www.mathnet.ru/eng/smj/v63/i1/p42
This publication is cited in the following 7 articles:
V. I. Bogachev, S. N. Popova, “Hausdorff distances between couplings and optimal transportation”, Sb. Math., 215:1 (2024), 28–51
Svetlana Popova, “Continuous selection of approximate Monge solutions in the Kantorovich problem with a parameter”, Funct. Anal. Appl., 58:2 (2024), 212–227
S. N. Popova, “O nelineinykh zadachakh Kantorovicha dlya funktsii stoimosti spetsialnogo vida”, Algebra i analiz, 36:4 (2024), 165–194
Svetlana N Popova, “On Uniqueness of an Optimal Solution to the Kantorovich Problem With Density Constraints”, International Mathematics Research Notices, 2024
Vladimir I. Bogachev, Svetlana N. Popova, “On Radon barycenters of measures on spaces of measures”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 44 (2023), 19–30
Vladimir I. Bogachev, Svetlana N. Popova, Airat V. Rezbaev, “On nonlinear Kantorovich problems with density constraints”, Mosc. Math. J., 23:3 (2023), 285–307
V. I. Bogachev, “Kantorovich problem of optimal transportation of measures: new directions of research”, Russian Math. Surveys, 77:5 (2022), 769–817
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