Published Paper

Inserted: 17 mar 2006
Last Updated: 27 jan 2007

Journal: Rend. Lincei - Mat. e Appl.
Volume: 18
Number: 1
Pages: 23 - 37
Year: 2007

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.

Keywords: Optimal transport, Wasserstein distance, Compressible Euler

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