Advanced Studies in Pure Mathematics

Optimal transportation of particles, fluids and currents

Yann Brenier

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In these lectures, we review a series of optimal transport (OT) problems of growing complexity. Surprisingly enough, in this seemingly narrow framework, we will encounter nonlinear PDEs of very different type, such as the Monge–Ampère équation, the Euler equations of incompressible fluids, the hydrostatic Boussinesq equations in convection theory, the Born–Infeld equation of electromagnetism, showing the hidden richness of the concept of optimal transportion

Article information

Variational Methods for Evolving Objects, L. Ambrosio, Y. Giga, P. Rybka and Y. Tonegawa, eds. (Tokyo: Mathematical Society of Japan, 2015), 59-85

Received: 10 August 2013
Revised: 14 October 2013
First available in Project Euclid: 19 October 2018

Permanent link to this document euclid.aspm/1539916033

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q
Secondary: 49 76

Optimal transport fluid mechanics electromagnetism


Brenier, Yann. Optimal transportation of particles, fluids and currents. Variational Methods for Evolving Objects, 59--85, Mathematical Society of Japan, Tokyo, Japan, 2015. doi:10.2969/aspm/06710059.

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