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

Article

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

Abstract

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)

49N9958E1791B25

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada