Optimal Transport for Applied Mathematicians Calculus of Variations, PDEs, and Modeling (eBook, 2015) [WorldCat.org]
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Optimal Transport for Applied Mathematicians Calculus of Variations, PDEs, and Modeling

Author: Filippo Santambrogio
Publisher: Cham Springer International Publishing :Imprint: Birkhäuser 2015
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Details

Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Filippo Santambrogio
ISBN: 9783319208282 3319208284 9783319208275 3319208276 9783319208299 3319208292 9783319365817 3319365819
OCLC Number: 1194489734
Description: 1 online resource
Responsibility: Filippo Santambrogio [aut]

Abstract:

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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