Svetlana Popova, “Continuous selection of approximate Monge solutions in the Kantorovich problem with a parameter”, Funktsional. Anal. i Prilozhen., 2024, Volume 58, Issue 2,Pages <nobr>137

Continuous selection of approximate Monge solutions in the Kantorovich problem with a parameter

Svetlana Popova^abc

^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

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.

MSC: 49Q22, 60B10

Received: 10.03.2023
Revised: 06.07.2023
Accepted: 22.07.2023

DOI: 10.4213/faa4106