Displaying similar documents to “How to show that some rays are maximal transport rays in Monge Problem”

On optimal matching measures for matching problems related to the Euclidean distance

José Manuel Mazón, Julio Daniel Rossi, Julián Toledo (2014)

Mathematica Bohemica

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We deal with an optimal matching problem, that is, we want to transport two measures to a given place (the target set) where they will match, minimizing the total transport cost that in our case is given by the sum of two different multiples of the Euclidean distance that each measure is transported. We show that such a problem has a solution with an optimal matching measure supported in the target set. This result can be proved by an approximation procedure using a p -Laplacian system....

On the hessian of the optimal transport potential

Stefán Ingi Valdimarsson (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We study the optimal solution of the Monge-Kantorovich mass transport problem between measures whose density functions are convolution with a gaussian measure and a log-concave perturbation of a different gaussian measure. Under certain conditions we prove bounds for the Hessian of the optimal transport potential. This extends and generalises a result of Caffarelli. We also show how this result fits into the scheme of Barthe to prove Brascamp-Lieb inequalities and thus prove a new generalised...