Geodesic
Path Functionals over Wasserstein Spaces
Journal of the European Mathematical Society, Tome 8 (2006) no. 3, pp. 415-434 Cet article a éte moissonné depuis la source EMS Press

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Given a metric space X we consider a general class of functionals which measure the cost of a path in X joining two given points x0​ and x1​, providing abstract existence results for optimal paths. The results are then applied to the case when X is a Wasserstein space of probabilities on a given set Ω and the cost of a path depends on the value of classical functionals over measures. Conditions to link arbitrary extremal measures μ0​ and μ1​ by means of finite cost paths are given.
DOI : 10.4171/jems/61
Classification : 49-XX, 58-XX, 90-XX, 00-XX
Keywords: Wasserstein distances, geodesics, irrigation trees, local functionals on measures 
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     author = {Alessio Brancolini and Giuseppe Buttazzo and Filippo Santambrogio},
     title = {Path {Functionals} over {Wasserstein} {Spaces}},
     journal = {Journal of the European Mathematical Society},
     pages = {415--434},
     year = {2006},
     volume = {8},
     number = {3},
     doi = {10.4171/jems/61},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/61/}
}
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Alessio Brancolini; Giuseppe Buttazzo; Filippo Santambrogio. Path Functionals over Wasserstein Spaces. Journal of the European Mathematical Society, Tome 8 (2006) no. 3, pp. 415-434. doi: 10.4171/jems/61

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