Advanced Studies in Pure Mathematics

Optimal transportation of particles, fluids and currents

Yann Brenier

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1539916033

Digital Object Identifier
doi:10.2969/aspm/06710059

Mathematical Reviews number (MathSciNet)
MR3587447

Zentralblatt MATH identifier
06701459

Subjects
Primary: 35Q
Secondary: 49 76

Keywords
Optimal transport fluid mechanics electromagnetism

Citation

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. https://projecteuclid.org/euclid.aspm/1539916033


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