Given a metric space we consider a general class of functionals which measure the cost of a path in joining two given points and , providing abstract existence results for optimal paths. The results are then applied to the case when is a Wasserstein space of probabilities on a given set and the cost of a path depends on the value of classical functionals over measures. Conditions to link arbitrary extremal measures and by means of finite cost paths are given.
Cite this article
Giuseppe Buttazzo, Alessio Brancolini, Filippo Santambrogio, Path Functionals over Wasserstein Spaces. J. Eur. Math. Soc. 8 (2006), no. 3, pp. 415–434DOI 10.4171/JEMS/61