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

DOI10.1090/S0002-9939-07-08877-6zbMath1120.49040OpenAlexW1582677256MaRDI QIDQ5308120

Chloe Jimenez, Guy Bouchitté, Mahadevan Rajesh

Publication date: 27 September 2007

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-07-08877-6

zbMATH Keywords

uniform estimatesWasserstein distanceoptimal transport map

Mathematics Subject Classification ID

PDEs of mixed type (35M10) Variational problems in a geometric measure-theoretic setting (49Q20)

Related Items (8)

\(L^\infty\) estimates in optimal mass transportation ⋮ Minimax confidence intervals for the sliced Wasserstein distance ⋮ \(L^\infty\)-estimates in optimal transport for non quadratic costs ⋮ Convergence in Law of the Maximum of the Two‐Dimensional Discrete Gaussian Free Field ⋮ On the structure of optimal transportation plans between discrete measures ⋮ \(L^\infty\)-optimal transport for a class of strictly quasiconvex cost functions ⋮ On the Pythagorean Structure of the Optimal Transport for Separable Cost Functions ⋮ An invariance principle for gradient flows in the space of probability measures

Cites Work

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• Interior \(W^{2,p}\) estimates for solutions of the Monge-Ampère equation
• The geometry of optimal transportation
• Asymptotic of an optimal location problem
• Constructing optimal maps for Monge’s transport problem as a limit of strictly convex costs
• Some regularity properties of solutions of Monge Ampère equation
• Differential equations methods for the Monge-Kantorovich mass transfer problem

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