Calculus of Variations and Partial Differential Equations

, Volume 43, Issue 3, pp 529-536

First online:

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

  • Brendan PassAffiliated withDepartment of Mathematics, University of Toronto Email author 

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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)

49N99 58E17 91B25