Weak regularity of Gauss mass transport

2009/04/12 by Alexander V. Kolesnikov, Kolesnikov, Alexander V.
Mathematics · #35J60 #49Q20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #math.AP #math.FA #msc:35J60 #msc:49Q20

paper · pdf · doi:10.48550/arxiv.0904.1852

31 pages; 40 references; new result on Sobolev estimates is added

openalex publication_date 2009/04/12 · arxiv created 2013/06/26 · arxiv updated 2013/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given two probability measures μ and ν we consider a mass transportation mapping T satisfying 1) T sends μ to ν, 2) T has the form T = ϕ(∇ ϕ)/(|∇ ϕ|), where ϕ is a function with convex sublevel sets. We prove a change of variables formula for T. We also establish Sobolev estimates for ϕ, and a new form of the parabolic maximum principle. In addition, we discuss relations to the Monge-Kantorovich problem, curvature flows theory, and parabolic nonlinear PDE's.

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