Displaying similar documents to “The Monge problem on non-compact manifolds”

Optimal mass transportation and Mather theory

Patrick Bernard, Boris Buffoni (2007)

Journal of the European Mathematical Society

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We study the Monge transportation problem when the cost is the action associated to a Lagrangian function on a compact manifold. We show that the transportation can be interpolated by a Lipschitz lamination. We describe several direct variational problems the minimizers of which are these Lipschitz laminations. We prove the existence of an optimal transport map when the transported measure is absolutely continuous. We explain the relations with Mather’s minimal measures.

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....

Optimal transportation networks as free Dirichlet regions for the Monge-Kantorovich problem

Giuseppe Buttazzo, Eugene Stepanov (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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In the paper the problem of constructing an optimal urban transportation network in a city with given densities of population and of workplaces is studied. The network is modeled by a closed connected set of assigned length, while the optimality condition consists in minimizing the Monge-Kantorovich functional representing the total transportation cost. The cost of trasporting a unit mass between two points is assumed to be proportional to the distance between them when the transportation...