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 this article
Luigi Ambrosio, Filippo Santambrogio, Necessary optimality conditions for geodesics in weighted Wasserstein spaces. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 18 (2007), no. 1, pp. 23–37DOI 10.4171/RLM/479