Moscow Mathematical Journal

Volume 23, Issue 3, July–September 2023 pp. 285–307.

On Nonlinear Kantorovich Problems with Density Constraints

Authors: Vladimir I. Bogachev (1), Svetlana N. Popova (2), and Airat V. Rezbaev (3)
Author institution:(1) Department of Mechanics and Mathematics, Moscow State University, 119991 Moscow, Russia;
National Research University Higher School of Economics, Myasnitskaya 20, 101000 Moscow, Russia;
Saint Tikhon's Orthodox University, Novokuznetskaya 23b, 115184 Moscow, Russia;
Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia
(2) Moscow Institute of Physics and Technology (State University), 9 Institutskiy per., 141700 Dolgoprudny, Moscow Region, Russia;
National Research University Higher School of Economics, Myasnitskaya 20, 101000 Moscow, Russia
(3) National Research University Higher School of Economics, Myasnitskaya 20, 101000 Moscow, Russia

Summary:

We study Kantorovich type optimal transportation problems that combine two new generalizations introduced and investigated recently by several authors: nonlinearity of cost functions, including dependence on conditional measures of transport plans, and constraints on densities of transport plans. New existence results are established and some counter-examples are constructed.

2020 Math. Subj. Class. 49N15, 49Q20, 28A33.

Keywords: Optimal transportation problem, nonlinear Kantorovich problem, density constraint, conditional measure.

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