Convexity inequalities and optimal transport of infinite-dimensional measures

DOI10.1016/j.matpur.2004.03.005zbMath1087.49034OpenAlexW2089833716MaRDI QIDQ1775750

Alexander V. Kolesnikov

Publication date: 4 May 2005

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matpur.2004.03.005

zbMATH Keywords

logarithmic gradientslog-Sobolev inequalityGaussian measuresoptimal transportMonge-Kantorovich problemTalagrand inequalityCameron-Martin spaceconvex measures

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20)

Related Items (12)

Hessian metrics, \(CD(K, N)\)-spaces, and optimal transportation of log-concave measures ⋮ Sobolev regularity for the Monge-Ampère equation in the Wiener space ⋮ Remarks on curvature in the transportation metric ⋮ Global Hölder estimates for optimal transportation ⋮ ON THE MONGE–AMPÈRE EQUATION IN INFINITE DIMENSIONS ⋮ From super Poincaré to weighted log-Sobolev and entropy-cost inequalities ⋮ Mass transport and variants of the logarithmic Sobolev inequality ⋮ On continuity equations in infinite dimensions with non-Gaussian reference measure ⋮ Sobolev estimates for optimal transport maps on Gaussian spaces ⋮ Sobolev regularity for the infinite-dimensional Monge-Ampère equation ⋮ On the Monge-Ampère equatin on Wiener space ⋮ On triangular mappings of Gaussian measures

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