Calculus of Variations and Geometric Measure Theory

T. Caillet

The five gradients inequality for non quadratic costs

created by caillet on 25 Mar 2023


Published Paper

Inserted: 25 mar 2023

Journal: Comptes Rendus. Mathématique
Volume: 361
Pages: 715-721
Year: 2023
Doi: 10.5802/crmath.444
Links: PDF


We give a proof of the "five gradients inequality" of Optimal Transportation Theory for general costs of the form $c(x,y)=h(x-y)$ where $h$ is a $C^1$ strictly convex radially symmetric function.