Exponential convergence of parabolic optimal transport on bounded domains

DOI10.2140/APDE.2020.13.2183zbMath1460.35217arXiv1812.04675OpenAlexW3105789538WikidataQ115497279 ScholiaQ115497279MaRDI QIDQ2657025

Farhan Abedin, Jun Kitagawa

Publication date: 17 March 2021

Published in: Analysis \& PDE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.04675

zbMATH Keywords

exponential convergenceoptimal mass transportMonge-KantorovichKim-McCann metricLi-Yau Harnack inequality

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for second-order parabolic equations (35K20) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Parabolic Monge-Ampère equations (35K96)

Related Items (1)

A Perturbative Approach to the Parabolic Optimal Transport Problem

Cites Work

• On the regularity of solutions of optimal transportation problems
• Gradient estimates for the heat equation under the Ricci flow
• Continuity, curvature, and the general covariance of optimal transportation
• On the parabolic kernel of the Schrödinger operator
• The geometry of optimal transportation
• On solutions to Cournot-Nash equilibria equations on the sphere
• Pseudo-Riemann geometry calibrates optimal transportation
• Regularity of potential functions of the optimal transportation problem
• A parabolic flow toward solutions of the optimal transportation problem on domains with boundary
• Parabolic Optimal Transport Equations on Manifolds
• On Harnack's inequality and entropy for the gaussian curvature flow
• On the second boundary value problem for Monge-Ampère type equations and optimal transportation
• Polar factorization and monotone rearrangement of vector‐valued functions
• On the second boundary value problem for equations of Monge-Ampère type.

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