Calculus of Variations and Geometric Measure Theory

A. Brancolini - G. Buttazzo - F. Santambrogio

Path Functionals over Wasserstein Spaces

created on 26 Sep 2017


Published Paper

Inserted: 26 sep 2017

Journal: J. Eur. Math. Soc.
Volume: 8
Number: 3
Pages: 415-434
Year: 2006
Doi: 10.4171/JEMS/61


Given a metric space $X$ we consider a general class of functionals which measure the cost of a path in $X$ joining two given points $x_0$ and $x_1$, providing abstract existence results for optimal paths. The results are then applied to the case when $X$ is a Wasserstein space of probabilities on a given set $\Omega$ and the cost of a path depends on the value of classical functionals over measures. Conditions to link arbitrary extremal measures $\mu_1$ and $\mu_2$ by means of finite cost paths are given.