Necessary optimality conditions for geodesics in weighted Wasserstein spaces

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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.
19 pages, submitted

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Analysis of PDEs, Classical Analysis and ODEs, 49K20; 76N10

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http://salesiana.dossiersoluciones.com/handle/123456789/110242

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0603435
 http://arxiv.org/abs/math/0603435

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arXiv