Necessary optimality conditions for geodesics in weighted Wasserstein spaces
Analysis of PDEs
2007-05-23 v1 Classical Analysis and ODEs
Abstract
The geodesic problem in Wasserstein spaces with a metric perturbed by a conformal factor is considered, and necessary optimality conditions are estabilished in a case where this conformal factor favours the spreading of the probability measure along the curve. These conditions have the form of a system of PDEs of the kind of the compressible Euler equations. Moreover, self-similar solutions to this system are discussed.
Cite
@article{arxiv.math/0603435,
title = {Necessary optimality conditions for geodesics in weighted Wasserstein spaces},
author = {Luigi Ambrosio and Filippo Santambrogio},
journal= {arXiv preprint arXiv:math/0603435},
year = {2007}
}
Comments
19 pages, submitted