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Necessary optimality conditions for geodesics in weighted Wasserstein spaces

Luigi Ambrosio·Filippo Santambrogio
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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.

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Luigi Ambrosio, Filippo Santambrogio. 2006-03-17. Necessary optimality conditions for geodesics in weighted Wasserstein spaces. https://arxiv.org/abs/math/0603435

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