The Monge Optimal Transportation Problem
نویسنده
چکیده
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 Monge problem [12] can be formulated as follows. For two given bounded open sets U and V in the Euclidean n-space, R, together with corresponding mass distributions with equal total mass, namely non-negative measures μ and ν on U and V satisfying the mass balance condition μ(U) = ν(V ) < ∞, whether there exists a measure preserving map s0 : U → V which minimizes the Monge cost functional
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