Calculus of Variations and Partial Differential Equations

, Volume 43, Issue 3, pp 529–536

On the local structure of optimal measures in the multi-marginal optimal transportation problem


DOI: 10.1007/s00526-011-0421-z

Cite this article as:
Pass, B. Calc. Var. (2012) 43: 529. doi:10.1007/s00526-011-0421-z


We consider an optimal transportation problem with more than two marginals. We use a family of semi-Riemannian metrics derived from the mixed, second order partial derivatives of the cost function to provide upper bounds for the dimension of the support of the solution.

Mathematics Subject Classification (2000)


Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada