Progress in Nonlinear Differential Equations and Their Applications

Optimal Transport for Applied Mathematicians

Calculus of Variations, PDEs, and Modeling

Authors: Santambrogio, Filippo

  • The role of optimal transport in applied mathematics is dramatically increasing, with applications in economics, finance, potential games, image processing and fluid dynamics 
  • Each chapter includes a section in which specific applications of optimal transport are discussed in relation to the mathematics presented 
  • Covers topics not found in other books on optimal transport, including the Knothe transport, the Dacorogna-Moser flow and the case of the supremal cost
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eBook 51,16 €
price for France (gross)
  • ISBN 978-3-319-20828-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 63,29 €
price for France (gross)
  • ISBN 978-3-319-20827-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.

Reviews

“This book is very well written, and the proofs are carefully chosen and adapted. It is suitable for the researcher or the student willing to enter this field as well as for the professor planning a course on this topic. Thanks to the discussions at the end of each chapter and to the rich bibliography it is also a very good reference book.” (Luigi De Pascale, Mathematical Reviews, January, 2017)


Table of contents (8 chapters)

  • Primal and dual problems

    Santambrogio, Filippo

    Pages 1-57

    Preview Buy Chapter 29,94 €
  • One-dimensional issues

    Santambrogio, Filippo

    Pages 59-85

    Preview Buy Chapter 29,94 €
  • L 1 and L ∞ theory

    Santambrogio, Filippo

    Pages 87-119

    Preview Buy Chapter 29,94 €
  • Minimal flows, divergence constraints, and transport density

    Santambrogio, Filippo

    Pages 121-175

    Preview Buy Chapter 29,94 €
  • Wasserstein distances and curves in the Wasserstein spaces

    Santambrogio, Filippo

    Pages 177-218

    Preview Buy Chapter 29,94 €

Buy this book

eBook 51,16 €
price for France (gross)
  • ISBN 978-3-319-20828-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 63,29 €
price for France (gross)
  • ISBN 978-3-319-20827-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Optimal Transport for Applied Mathematicians
Book Subtitle
Calculus of Variations, PDEs, and Modeling
Authors
Series Title
Progress in Nonlinear Differential Equations and Their Applications
Series Volume
87
Copyright
2015
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-20828-2
DOI
10.1007/978-3-319-20828-2
Hardcover ISBN
978-3-319-20827-5
Series ISSN
1421-1750
Edition Number
1
Number of Pages
XXVII, 353
Topics