On the Monge mass transfer problem

By Neil S. Trudinger, Xu-jia Wang. 2001

148 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/953814fbe28e68fac82af396094f6833aced75ea

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Monge problem in metric measure spaces with Riemannian curvature-dimension condition (2013, unknown): “After that, many results reduced the assumptions on the supports of μ0, μ1, see [6] and [26].”
Optimal transport maps in Monge-Kantorovich problem (2003, methodology): “The proof in [3], instead, uses the co-area formula to show that absolute continuity with respect to Lebesgue measure is stable under disintegration.”
Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling (2015, methodology): “obtained by Evans-Gangbo, [160] (via a method which is linked to what we will see in Chapter 4, and unfortunately under stronger assumptions on the densities) and by Caffarelli-Feldman-McCann, [102] and, independently, Trudinger-Wang, [291], via an approximation through strictly convex costs.”
Monge's transport problem on a Riemannian manifold (2001, methodology): “The proof of this estimate is a main technical difficulty distinguishing the present Riemannian problem from the Euclidean case studied in [3] and [19].”
The Monge problem for strictly convex norms in Rd (2010, unknown): “[28] for μ and ν with integrable density.”
Monge’s problem with a quadratic cost by the zero-noise limit of h-path processes (2004, unknown): “…for which the Euler-Lagrange equation is the p - Laplacian PDE under the assumption that P 0 and P 1 have disjoint compact supports, and in [6] and [24] they studied (1.2) by the “ q ↓ 1” limit of (1.2) with L ( u ) = | u | q under the assumption that P 0 and P 1 have compact supports (see also…”
Existence and stability results in the L 1 theory of optimal transportation (2003, background): “Afterwards, the first author estabilished in [3] the existence of an optimal transport map assuming only that the initial measure µ is absolutely continuous, and the results of [16] and [ 42 ] have been extended to a Riemannian setting in [28].”
On the design of a reflector antenna II (2004, background): “For Monge’s cost function the existence of optimal mappings was not proved until recently in [2,8,19].”
Optimal transportation, topology and uniqueness (2010, background): “Adding further restrictions beyond this twist hypothesis allowed Ma, Trudinger, Wang [72] [100], and later Loeper [68], to develop a regularity theory for the map f1 : X −→ Y , embracing Delanoë [36], Caffarelli [20] [21] and Urbas’ [102] results for the quadratic cost, Gangbo and McCann’s for its ”
Uniqueness and transport density in Monge's mass transportation problem (2002, methodology): “Thus it would seem that Evans and Gangbo [9] contains the the first complete proof of existence for optimal maps between Lipschitz densities f± with disjoint support, while Caffarelli-Feldman-McCann [6] and Trudinger-Wang [30] contain the first complete proofs for more general f± ∈ L1(Rn).”
A User’s Guide to Optimal Transport (2013, background): “Gangbo [34], Trudinger and Wang [78], and L.”
Constructing optimal maps for Monge's transport problem as a limit of strictly convex costs (2001, background): “Foremost among them is the concurrent but independent discovery of a existence result for optimal maps in Monge’s problem by Trudinger and Wang [24].”
Free boundaries in optimal transport and Monge-Ampere obstacle problems (2010, background): “x; y/ D jx yj in particular has attracted recent attention from Ambrosio [7] and Pratelli [9], Ambrosio, Kircheim and Pratelli [5], Caffarelli, Feldman and McCann [20], DePascale, Evans and Pratelli [30], Feldman and McCann [37], [36], and Trudinger and Wang [76] following the work of Evans and Gang”