Path Functionals over Wasserstein Spaces

  • Giuseppe Buttazzo

    Università di Pisa, Italy
  • Alessio Brancolini

    Politecnico di Bari, Italy
  • Filippo Santambrogio

    Scuola Normale Superiore, Pisa, Italy


Given a metric space XX we consider a general class of functionals which measure the cost of a path in XX joining two given points x0x_0 and x1x_1, providing abstract existence results for optimal paths. The results are then applied to the case when XX is a Wasserstein space of probabilities on a given set Ω\Omega and the cost of a path depends on the value of classical functionals over measures. Conditions to link arbitrary extremal measures μ0\mu_0 and μ1\mu_1 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. 415–434

DOI 10.4171/JEMS/61