A new $L^\infty$ estimate in optimal mass transport

Autor:	M. Rajesh, Chloé Jimenez, Guy Bouchitté
Rok vydání:	2007
Předmět:	Pure mathematics Mass transport Applied Mathematics General Mathematics 010102 general mathematics Geometry Absolute continuity Lipschitz continuity 01 natural sciences Infimum and supremum 010101 applied mathematics Displacement mapping Geography Bounded function 0101 mathematics
Zdroj:	Proceedings of the American Mathematical Society. 135:3525-3536
ISSN:	0002-9939
Popis:	Let Ω be a bounded Lipschitz regular open subset of R d and let μ,ν be two probablity measures on Ω. It is well known that if μ= f dx is absolutely continuous, then there exists, for every p > 1, a unique transport map Tp pushing forward μ on v and which realizes the Monge-Kantorovich distance Wp(μ, ν). In this paper, we establish an L°° bound for the displacement map T p x-x which depends only on p, on the shape of Ω and on the essential infimum of the density f.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::3422de83963a12469eb321b2b7d449b0 https://doi.org/10.1090/s0002-9939-07-08877-6 Zobrazit plný text záznamu