Optimal Transport for Applied Mathematicians

Calculus of Variations, PDEs, and Modeling

  • Filippo Santambrogio

Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 87)

Table of contents

  1. Front Matter
    Pages i-xxvii
  2. Filippo Santambrogio
    Pages 1-57
  3. Filippo Santambrogio
    Pages 59-85
  4. Filippo Santambrogio
    Pages 87-119
  5. Filippo Santambrogio
    Pages 219-248
  6. Filippo Santambrogio
    Pages 249-284
  7. Filippo Santambrogio
    Pages 285-323
  8. Back Matter
    Pages 325-353

About this book


This monograph presents a rigorous mathematical introduction to optimal transport as a variational problem, its use in modeling various phenomena, and its connections with partial differential equations. Its main goal is to provide the reader with the techniques necessary to understand the current research in optimal transport and the tools which are most useful for its applications. Full proofs are used to illustrate mathematical concepts and each chapter includes a section that discusses applications of optimal transport to various areas, such as economics, finance, potential games, image processing and fluid dynamics. Several topics are covered that have never been previously in books on this subject, such as the Knothe transport, the properties of functionals on measures, the Dacorogna-Moser flow, the formulation through minimal flows with prescribed divergence formulation, the case of the supremal cost, and the most classical numerical methods. Graduate students and researchers in both pure and applied mathematics interested in the problems and applications of optimal transport will find this to be an invaluable resource.


Fluid mechanics Fokker-Planck equation Gradient Flows Measure Theory Monge-Ampère equation Optimal transport Partial differential equations

Authors and affiliations

  • Filippo Santambrogio
    • 1
  1. 1.Laboratoire de Mathématiques d’OrsayUniversité Paris-SudOrsay cedexFrance

Bibliographic information