Overview
- 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
Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 87)
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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.
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Keywords
Table of contents (8 chapters)
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Front Matter
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Back Matter
Reviews
“This book offers an excellent, exciting and enjoyable, tour through the theory of optimal transportation, with a very good choice of topics … . It is well written and thorough and provides an excellent introduction to applied mathematicians … . a carefully selected list of exercises, make it ideal either as a textbook for an advanced postgraduate of doctoral level course, or for independent study.” (Athanasios Yannacopoulos, zbMATH 1401.49002, 2019)
“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)
“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)
Authors and Affiliations
Bibliographic Information
Book Title: Optimal Transport for Applied Mathematicians
Book Subtitle: Calculus of Variations, PDEs, and Modeling
Authors: Filippo Santambrogio
Series Title: Progress in Nonlinear Differential Equations and Their Applications
DOI: https://doi.org/10.1007/978-3-319-20828-2
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Hardcover ISBN: 978-3-319-20827-5Published: 27 October 2015
Softcover ISBN: 978-3-319-36581-7Published: 23 August 2016
eBook ISBN: 978-3-319-20828-2Published: 17 October 2015
Series ISSN: 1421-1750
Series E-ISSN: 2374-0280
Edition Number: 1
Number of Pages: XXVII, 353
Topics: Calculus of Variations and Optimal Control; Optimization, Ordinary Differential Equations, Partial Differential Equations, Measure and Integration