Path Functionals over Wasserstein Spaces

• Autores: Alessio Brancolini, Giuseppe Buttazzo, Filippo Santambrogio
• Localización: Journal of the European Mathematical Society, ISSN 1435-9855, Vol. 8, Nº 3, 2006, págs. 415-434
• Idioma: inglés
• DOI: 10.4171/jems/61
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• Resumen

  • 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.