On nonlinear Kantorovich problems for cost functions of special form

Kantorovich type optimal transportation problems with nonlinear cost functions are treated, including the dependence on conditional measures of transport plans. A range of nonlinear Kantorovich problems for cost functions of a special form is considered and results on the existence (or nonexistence) of optimal solutions are proved. The relationshp is established between the nonlinear Kantorovich problem with the cost function of some special form and the Monge problem with convex dominance.