Lipschitz estimates on the JKO scheme for the Fokker-Planck equation on bounded convex domains

DOI10.1016/j.aml.2020.106806zbMath1454.35385arXiv2007.08192OpenAlexW3092479816MaRDI QIDQ2213737

Vincent Ferrari, Filippo Santambrogio

Publication date: 3 December 2020

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.08192

zbMATH Keywords

optimal transportgradient flowslinear diffusionBakry-Emery estimates

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Fokker-Planck equations (35Q84)

Related Items

The flow map of the Fokker-Planck equation does not provide optimal transport ⋮ JKO estimates in linear and non-linear Fokker-Planck equations, and Keller-Segel: \(L^p\) and Sobolev bounds

Cites Work

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• The Monge-Ampère equation and its applications
• \{Euclidean, metric, and Wasserstein\} gradient flows: an overview
• Weighted ultrafast diffusion equations: from well-posedness to long-time behaviour
• On the Jordan-Kinderlehrer-Otto scheme
• Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling
• The Monge–Ampère equation and its link to optimal transportation
• Some regularity properties of solutions of Monge Ampère equation
• The Variational Formulation of the Fokker--Planck Equation
• Analysis and Geometry of Markov Diffusion Operators
• \(BV\) estimates in optimal transportation and applications