A superlinear multifunction arising in connection with mass transfer problems

Given a nonempty set X, we consider all cost functions c: X x X --> R(1) boolean OR {+infinity} and take the multifunction Q(0)(c) := {u is an element of R(X): u(x) - u(y) less than or equal to c(x, y) for all x, y is an element of X} that arises in connection with mass transfer problems generalizing the classical Monge-Kantorovich problem. We study properties of the multifunction including conditions on c for Q(0)(c) to be nonempty and characterizations of Q(0)(c) for a given c. Applications are given to cyclically monotone operators and to dynamic optimization.