We investigate the approximation of the Monge problem (minimizing Ω |T (x) − x|dµ(x) among the vector-valued maps T with prescribed image measure T#µ) by adding a vanishing Dirichlet energy, namely ε Ω |DT |2. We study the Γ-convergence as ε → 0, proving a density result for Sobolev (or Lipschitz) transport maps in the class of transport plans. In a certain two-dimensional framework that we analyze in details, when no optimal plan is induced by an H1 map, we study the selected limit map, which is a new special Monge transport, possibly different from the monotone one, and we find the precise asymptotics of the optimal cost depending on ε, where the leading term is of order ε | log ε|
We design a monotone finite difference discretization of the second boundary value problem for the M...
AbstractThe aim of this article is to show that the Monge–Kantorovich problem is the limit, when a f...
This short contribution summarizes a talk given on May 5, 2010, in Cairo, describing some unexpected...
We investigate the approximation of the Monge problem (minimizing \int_Ω |T (x) − x| dµ(x) among the...
We study the entropic regularization of the optimal transport problem in dimension 1 when the cost f...
The Monge problem in R^n, with a possibly asymmetric norm cost function and absolutely continuous fi...
International audienceWe study the entropic regularization of the optimal transport problem in dimen...
order variational heuristics for the Monge problem on compact manifolds∗ Ph. Delanoë† We consider M...
Le problème du transport optimal, originellement introduit par Monge au 18ème siècle, consiste à min...
The optimal transportation problem was originally introduced by Monge in the 18th century; it consi...
In this paper we study the dimension of some measures which are related to the classical Monge's opt...
Abstract. We provide counterexamples to regularity of optimal maps in the classical Monge problem un...
In this thesis we study the regularity problem in optimal transportation, by establishing the a prio...
We provide counterexamples to regularity of optimal maps in the classical Monge problem under variou...
On montre l'existence d'une application de transport optimale pour le problème de Monge lorsque le c...
We design a monotone finite difference discretization of the second boundary value problem for the M...
AbstractThe aim of this article is to show that the Monge–Kantorovich problem is the limit, when a f...
This short contribution summarizes a talk given on May 5, 2010, in Cairo, describing some unexpected...
We investigate the approximation of the Monge problem (minimizing \int_Ω |T (x) − x| dµ(x) among the...
We study the entropic regularization of the optimal transport problem in dimension 1 when the cost f...
The Monge problem in R^n, with a possibly asymmetric norm cost function and absolutely continuous fi...
International audienceWe study the entropic regularization of the optimal transport problem in dimen...
order variational heuristics for the Monge problem on compact manifolds∗ Ph. Delanoë† We consider M...
Le problème du transport optimal, originellement introduit par Monge au 18ème siècle, consiste à min...
The optimal transportation problem was originally introduced by Monge in the 18th century; it consi...
In this paper we study the dimension of some measures which are related to the classical Monge's opt...
Abstract. We provide counterexamples to regularity of optimal maps in the classical Monge problem un...
In this thesis we study the regularity problem in optimal transportation, by establishing the a prio...
We provide counterexamples to regularity of optimal maps in the classical Monge problem under variou...
On montre l'existence d'une application de transport optimale pour le problème de Monge lorsque le c...
We design a monotone finite difference discretization of the second boundary value problem for the M...
AbstractThe aim of this article is to show that the Monge–Kantorovich problem is the limit, when a f...
This short contribution summarizes a talk given on May 5, 2010, in Cairo, describing some unexpected...