Vladimir I. Bogachev, Svetlana N. Popova, Airat V. Rezbaev, “On nonlinear Kantorovich problems with density constraints”, Mosc. Math. J., 2023, Volume 23, Number 3,Pages <nobr>285

This article is cited in 2 papers

On nonlinear Kantorovich problems with density constraints

Vladimir I. Bogachev^abcd, Svetlana N. Popova^ed, Airat V. Rezbaev^d

^a Department of Mechanics and Mathematics, Moscow State University, 119991 Moscow, Russia
^b Saint Tikhon's Orthodox University, Novokuznetskaya 23b, 115184 Moscow, Russia
^c Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia
^d National Research University Higher School of Economics, Myasnitskaya 20, 101000 Moscow, Russia
^e Moscow Institute of Physics and Technology (State University), 9 Institutskiy per., 141700 Dolgoprudny, Moscow Region, Russia

Abstract: 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.

Key words and phrases: optimal transportation problem, nonlinear Kantorovich problem, density constraint, conditional measure.

MSC: 49N15, 49Q20, 28A33

Language: English