Optimal transport and large number of particles

Wilfrid Gangbo; Andrzej Świech

doi:10.3934/dcds.2014.34.1397

Article Contents

2014, Volume 34, Issue 4: 1397-1441. Doi: 10.3934/dcds.2014.34.1397

This issue Previous Article On the Lagrangian structure of quantum fluid models Next Article Metric cycles, curves and solenoids

Optimal transport and large number of particles

Wilfrid Gangbo^1, and
Andrzej Świech^1,

1.
School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, GA 30332-0160

Received: December 31, 2012

Revised: March 31, 2013

Published: March 2014

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Abstract

We present an approach for proving uniqueness of ODEs in the Wasserstein space. We give an overview of basic tools needed to deal with Hamiltonian ODE in the Wasserstein space and show various continuity results for value functions. We discuss a concept of viscosity solutions of Hamilton-Jacobi equations in metric spaces and in some cases relate it to viscosity solutions in the sense of differentials in the Wasserstein space.

Keywords:

Optimal transport,
conservative systems,
infinite dimensional Hamiltonian systems,
Hamilton-Jacobi equations.

Mathematics Subject Classification: Primary: 35F21, 37K05, 49L25; Secondary: 76A99.

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