JournalsrlmVol. 18, No. 1pp. 23–37

Necessary optimality conditions for geodesics in weighted Wasserstein spaces

  • Luigi Ambrosio

    Scuola Normale Superiore, Pisa, Italy
  • Filippo Santambrogio

    Scuola Normale Superiore, Pisa, Italy
Necessary optimality conditions for geodesics in weighted Wasserstein spaces cover
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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 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. 23–37

DOI 10.4171/RLM/479