Calculus of Variations and Geometric Measure Theory

L. Ambrosio - F. Santambrogio

Necessary optimality conditions for geodesics in weighted Wasserstein spaces

created by ambrosio on 17 Mar 2006
modified by santambro on 27 Jan 2007


Published Paper

Inserted: 17 mar 2006
Last Updated: 27 jan 2007

Journal: Rend. Lincei - Mat. e Appl.
Volume: 18
Number: 1
Pages: 23 - 37
Year: 2007


The geodesic problem in Wasserstein spaces with a metric perturbed by a conformal factor is considered, and necessary optimality conditions are estabilished in a case where this conformal factor favours the spreading of the probability measure along the curve. These conditions have the form of a system of PDEs of the kind of the compressible Euler equations. Moreover, self-similar solutions to this system are discussed.

Keywords: Optimal transport, Wasserstein distance, Compressible Euler