# Path functionals over Wasserstein spaces

Alessio Brancolini; Giuseppe Buttazzo; Filippo Santambrogio

Journal of the European Mathematical Society (2006)

- Volume: 008, Issue: 3, page 415-434
- ISSN: 1435-9855

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topBrancolini, 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 -

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