Path functionals over Wasserstein spaces

Brancolini A., Buttazzo G., Santambrogio F.

Zusammenfassung

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 X0 and x1, 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 Ω and the cost of a path depends on the value of classical functionals over measures. Conditions for linking arbitrary extremal measures μ0 and μ1 by means of finite cost paths are given. © European Mathematical Society 2006.