Inserted: 17 mar 2006
Last Updated: 27 jan 2007
Journal: Rend. Lincei - Mat. e Appl.
Pages: 23 - 37
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