Extended Monge-Kantorovich Theory

By Yann Brenier. 2003

168 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c4e7a47b1d454dccb464370679f7a711c8fefb22

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Citations in the corpus

Kantorovich Metric: Initial History and Little-Known Applications (2005, methodology): “ the case p = 2 is much more convenient from the technical and geometric point of view. The corresponding variational problem and Euler equation are simpler than in the case p = 1, and the results of [2] show that for a certain geometric transportation problem, the Euler equation is the well-known M”
Optimal mass transportation and Mather theory (2004, background): “2 Currents This formulation finds its roots on one hand in the works of Benamou and Brenier, see [6], and then Brenier, see [13], and on the other hand in the work of Bangert [5].”
The Cauchy problem for a strongly degenerate quasilinear equation (2005, methodology): “As Brenier pointed out in [14], this relativistic heat equation”
Regularity of Potential Functions of the Optimal Transportation Problem (2005, background): “We show that (A3) is satisfied by the two important cost functions [5], c(x, y) = √ 1− |x− y|2 and c(x, y) = √ 1 + |x− y|2; and more generally by the cost function”
Nonlinear mobility continuity equations and generalized displacement convexity (2009, methodology): “As in [7], we insert the nonlinear mobility continuity equation (1.”
Young measures, superposition and transport (2007, unknown): “D S] 9 J ul 2 00 Published in: Indiana University Math Journal, 57 No 1 (2008) pp 247–276.”
Convexity properties of Dirichlet integrals and Picone-type inequalities (2014, background): “This simple remark is the crucial ingredient of the so-called Benamou-Brenier formula for the 2−Wasserstein distance (see [4, 9]).”
{Euclidean, metric, and Wasserstein} gradient flows: an overview (2016, background): “This iswhat is usually calledBenamou– Brenier formula (see [11] for the quadratic case, and [21] for a general introduction).”