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Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling (Progress in Nonlinear Differential Equations and Their Applications, 87) - Softcover

Book 43 of 53: Progress in Nonlinear Differential Equations and Their Applications

Santambrogio, Filippo

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9783319365817: Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling (Progress in Nonlinear Differential Equations and Their Applications, 87)
Softcover
ISBN 10: 3319365819 ISBN 13: 9783319365817
Publisher: Birkhäuser, 2016

Synopsis

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.

"synopsis" may belong to another edition of this title.

From the Back Cover

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.

"About this title" may belong to another edition of this title.

Publisher
Birkhäuser
Publication date
2016
Language
English
ISBN 10 
3319365819
ISBN 13 
9783319365817
Binding
Paperback
Rating
  • 4.29 out of 5 stars
    7 ratings by Goodreads