In this paper we extend the scope of Caffarelli’s contraction theorem, which provides a measure of the Lipschitz constant for optimal transport maps between log-concave probability densities in \mathbb{R}^{d} . Our focus is on a broader category of densities, specifically those that are \frac{1}{d} -concave and can be represented as V^{-d} , where V is convex. By setting appropriate conditions, we derive linear or sublinear limitations for the optimal transport map. This leads us to a comprehensive Lipschitz estimate that aligns with the principles established in Caffarelli’s theorem.

Guillaume Carlier

Alessio Figalli

Filippo Santambrogio

Annales de l Institut Henri Poincaré C Analyse Non Linéaire

The Nonlinear Analysis section of the Annales de l'Institut Henri Poincaré is an international journal created in 1983 which publishes original and high quality research articles. It concentrates on all domains concerned with nonlinear analysis, specially applicable to PDE, mechanics, physics, economy, without overlooking the numerical aspects.

The Annales de l'Institut Henri Poincaré (C) Analyse Non Lineaire is an international journal established in 1983, focusing on the field of nonlinear analysis. It publishes original and high-quality research articles that cover all domains related to nonlinear analysis, particularly applicable to partial differential equations, mechanics, physics, and economics, while also addressing numerical aspects.

《Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire》是一本国际期刊，成立于1983年，专注于非线性分析领域，发表原创且高质量的研究文章。期刊涵盖与非线性分析相关的所有领域，特别是偏微分方程、力学、物理学和经济学等应用，同时也关注数值分析的相关内容。

Category	Quartile
数学	1
数学, 应用数学	1

On optimal transport maps between $\frac{1}{d}$-concave densities

ivySCI AI Smartly Parses PDF, Answers Researchers' Questions, and Helps You Understand Papers in Seconds

Journal Info

Category	Quartile
MATHEMATICS, APPLIED	1