30 apr 2008

**Abstract.**

We study Monge optimal transportation problem where the cost function is the cost of an optimal control problem and try to understand what are natural regularity conditions which would allow to extend well-known results of Brenier and McCann on the existence, uniqueness and characterization of solutions. It happens that optimal control approach works well for a wide class of Carnot-Caratheodory spaces with the cost given by the square of the distance and thus provides a generalization of the results of L. Ambrosio and S. Rigot on the Heisenberg group. This is a joint work with P.Lee, Toronto