Calculus of Variations and Geometric Measure Theory

G. Savaré - G. E. Sodini

A simple relaxation approach to duality for Optimal Transport problems in completely regular spaces

created by sodini on 17 Jun 2022
modified on 24 Jun 2022


Published Paper

Inserted: 17 jun 2022
Last Updated: 24 jun 2022

Journal: Journal of Convex Analysis
Volume: 29
Number: 1
Pages: 1-12
Year: 2022


We present a simple and direct approach to duality for Optimal Transport for lower semicontinuous cost functionals in arbitrary completely regular topological spaces, showing that the Optimal Transport functional can be interpreted as the largest sublinear and weakly lower semicontinuous functional extending the cost between pairs of Dirac masses.