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Optimal transportation under nonholonomic constraints

TitleOptimal transportation under nonholonomic constraints
Publication TypeJournal Article
Year of Publication2009
AuthorsAgrachev, AA, Lee, P
JournalTrans. Amer. Math. Soc. 361 (2009) 6019-6047

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.

Alternate JournalControl theory and optimal mass transport

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