Optimal transport for applied mathematicians : calculus of variations, PDEs, and modeling (Book, 2015) [WorldCat.org]
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Optimal transport for applied mathematicians : calculus of variations, PDEs, and modeling

Author: Filippo Santambrogio
Publisher: Cham : Springer, 2015.
Series: Progress in nonlinear differential equations and their applications, 87
Edition/Format:   Print book : 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.℗ℓIts 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.℗ℓFull proofs are used to  Read more...
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Details

Document Type: Book
All Authors / Contributors: Filippo Santambrogio
ISBN: 9783319208275 3319208276
OCLC Number: 1010580201
Description: xxvii, 353 pages : illustrations ; 25 cm
Contents: Preface --
Primal and Dual Problems --
One-Dimensional Issues --
L^1 and L^infinity Theory.-℗ℓMinimal Flows.-℗ℓWasserstein Spaces --
Numerical Methods --
Functionals over Probabilities.-℗ℓGradient Flows --
Exercises --
References --
Index.℗ℓ℗ℓ℗ℓ℗ℓ.
Series Title: Progress in nonlinear differential equations and their applications, 87
Responsibility: Filippo Santambrogio.

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.℗ℓIts 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.℗ℓFull 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.℗ℓSeveral 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℗ℓminimal flows with prescribed divergence formulation, the case of the supremal cost, and the most classical numerical methods.℗ℓGraduate 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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