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Path functionals over Wasserstein spaces

Alessio Brancolini, Giuseppe Buttazzo, Filippo Santambrogio (2006)

Journal of the European Mathematical Society

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 aWasserstein 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 μ 0 and μ 1 by means of finite cost paths are given.

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