OPTIMAL TRANSPORTATION UNDER NONHOLONOMIC CONSTRAINTS

We study Mongs's optimal transportation problem. where the cost, is given by an optimal control cost We prove the existence and uniqueness of all optimal map under certain regularly conditions oil the Lagrangian, absolute continuity of the measures with respect to Lebesgue, and most importantly the absence of sharp abnormal minimizers In particular, this result is applicable in the case of subriemannian manifolds with a 2-generating distribution and cost given by d(2), where d is the subriemannian distance Also, we discuss sonic properties of the optimal plan when abnormal minimizers are present Finally we consider Some examples of displacement Interpolation in the case of the Grushin plane