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 $\mu_0$ and $\mu_1$ by means of finite cost paths are given.

Path functionals over Wasserstein spaces

BUTTAZZO, GIUSEPPE;
2006-01-01

Abstract

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 $\mu_0$ and $\mu_1$ by means of finite cost paths are given.
2006
A., Brancolini; Buttazzo, Giuseppe; F., Santambrogio
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/100594
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