Regularity Properties of Monotone Measure-preserving Maps

2023/05/15 by Alessio Figalli, Figalli, Alessio, Yash Jhaveri +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2305.09001

openalex publication_date 2023/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we extend the regularity theory for monotone measure-preserving maps, also known as optimal transports for the quadratic cost optimal transport problem, to the case when the support of the target measure is an arbitrary convex domain and, on the low-regularity end, between domains carrying certain invariant measures.

Related

• Regularity of monotone transport maps between unbounded domains
• Global regularity of optimal mappings in non-convex domains
• Existence and uniqueness of optimal transport maps
• Monotone Measure-Preserving Maps in Hilbert Spaces: Existence, Uniqueness, and Stability
• Partial Regularity for optimal transport maps