Path functionals over Wasserstein spaces

Brancolini, Alessio, Buttazzo, Giuseppe, and Santambrogio, Filippo. "Path functionals over Wasserstein spaces." Journal of the European Mathematical Society 008.3 (2006): 415-434. <http://eudml.org/doc/277501>.

@article{Brancolini2006,
abstract = {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 $\Omega $ and the cost of a path depends on the value of classical functionals over measures. Conditions for linking arbitrary extremal measures $\mu _0$ and $\mu _1$ by means of finite cost paths are given.},
author = {Brancolini, Alessio, Buttazzo, Giuseppe, Santambrogio, Filippo},
journal = {Journal of the European Mathematical Society},
keywords = {Wasserstein distances; geodesics; irrigation trees; local functionals on measures; Wasserstein distances; geodesics; irrigation trees; local functionals on measures},
language = {eng},
number = {3},
pages = {415-434},
publisher = {European Mathematical Society Publishing House},
title = {Path functionals over Wasserstein spaces},
url = {http://eudml.org/doc/277501},
volume = {008},
year = {2006},
}

TY - JOUR
AU - Brancolini, Alessio
AU - Buttazzo, Giuseppe
AU - Santambrogio, Filippo
TI - Path functionals over Wasserstein spaces
JO - Journal of the European Mathematical Society
PY - 2006
PB - European Mathematical Society Publishing House
VL - 008
IS - 3
SP - 415
EP - 434
AB - 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 $\Omega $ and the cost of a path depends on the value of classical functionals over measures. Conditions for linking arbitrary extremal measures $\mu _0$ and $\mu _1$ by means of finite cost paths are given.
LA - eng
KW - Wasserstein distances; geodesics; irrigation trees; local functionals on measures; Wasserstein distances; geodesics; irrigation trees; local functionals on measures
UR - http://eudml.org/doc/277501
ER -