منابع مشابه
The Monge Optimal Transportation Problem
We report here two recent developments in the theory of optimal transportation. The first is a proof for the existence of optimal mappings to the Monge mass transportation problem [16]. The other is an application of optimal transportation in geometric optics [19]. The optimal transportation problem, in general, deals with the redistribution of materials in the most economical way. The original...
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We transfer the celebrating Monge-Kontorovich problem in a bounded domain of Euclidean plane into a Dirichlet boundary problem associated to a quasi-linear elliptic equation with 0−order term missing in its diffusion coefficients: A(x, F ′ x )F ′′ xx +B(y, F ′ y )F ′′ yy = C(x, y, F ′ x , F ′ y ) where A(., .) > 0, B(., .) > 0 and C are functions based on the initial distributions, F is an unkn...
متن کاملThe Monge Problem in Geodesic Spaces
We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish non branching geodesic space. We show that we can reduce the transport problem to 1-dimensional transport problems along geodesics. We introduce an assumption on the transport problem π which implies that the conditional probabilities of the first marginal on each geodesic are continuous. It is known that...
متن کاملThe Monge Problem in Wiener Space
We address the Monge problem in the abstract Wiener space and we give an existence result provided both marginal measures are absolutely continuous with respect to the infinite dimensional Gaussian measure γ.
متن کاملMultivariate Monge-Kantorovich Transportation Problem
Received: January 6, 2011 Accepted: January 24, 2011 doi:10.5539/jmr.v3n2p66 The research is supported by Zhejiang Provincial Education Department research projects (Y201016421) Abstract Monge-Kantorovich transportation problem in a bounded region of Euclidean space is transferred into a partial differential equations group. And then the explicit formula of the optimal coupling is achieved. The...
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2011
ISSN: 0012-7094
DOI: 10.1215/00127094-1272939