Global Hölder estimates for optimal transportation

DOI10.1134/S0001434610110076zbMath1236.49087arXiv0810.5043OpenAlexW2073480697MaRDI QIDQ650335

Alexander V. Kolesnikov

Publication date: 25 November 2011

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0810.5043

zbMATH Keywords

modulus of convexityGaussian measureHölder estimateLipschitz mappingoptimal transportation of measures

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Set-valued set functions and measures; integration of set-valued functions; measurable selections (28B20) Variational problems in a geometric measure-theoretic setting (49Q20)

Related Items (6)

Hessian metrics, \(CD(K, N)\)-spaces, and optimal transportation of log-concave measures ⋮ A proof of the Caffarelli contraction theorem via entropic regularization ⋮ A generalization of Caffarelli's contraction theorem via (reverse) heat flow ⋮ Entropic-Wasserstein Barycenters: PDE Characterization, Regularity, and CLT ⋮ On continuity equations in infinite dimensions with non-Gaussian reference measure ⋮ Sobolev estimates for optimal transport maps on Gaussian spaces

Cites Work

• Boundary regularity of maps with convex potentials. II
• Mass transport and variants of the logarithmic Sobolev inequality
• Oblique boundary value problems for equations of Monge-Ampère type
• From Brunn-Minkowski to Brascamp-Lieb and to logarithmic Sobolev inequalities
• A convex/log-concave correlation inequality for Gaussian measure and an application to abstract Wiener spaces
• Convexity inequalities and optimal transport of infinite-dimensional measures
• Lévy-Gromov's isoperimetric inequality for an infinite dimensional diffusion generator
• Transportation cost for Gaussian and other product measures
• An isoperimetric inequality for uniformly log-concave measures and uniformly convex bodies
• The Regularity of Mappings with a Convex Potential
• Monotonicity properties of optimal transportation and the FKG and related inequalities
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