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 -