TY - JOUR T1 - Optimal transportation under nonholonomic constraints JF - Trans. Amer. Math. Soc. 361 (2009) 6019-6047 Y1 - 2009 A1 - Andrei A. Agrachev A1 - Paul Lee AB - We study the Monge\\\'s optimal transportation problem where the cost is given by optimal control cost. We prove the existence and uniqueness of optimal map under certain regularity conditions on the Lagrangian, absolute continuity of the measures and most importantly the absent 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 d2, where d is the subriemannian distance. Also, we discuss some properties of the optimal plan when abnormal minimizers are present. Finally, we consider some examples of displacement interpolation in the case of Grushin plane. UR - http://hdl.handle.net/1963/2176 U1 - 2068 U2 - Mathematics U3 - Functional Analysis and Applications ER -