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

Buch 43 von 53: Progress in Nonlinear Differential Equations and Their Applications

Santambrogio, Filippo

 
9783319208275: Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling (Progress in Nonlinear Differential Equations and Their Applications, 87, Band 87)
Hardcover
ISBN 10: 3319208276 ISBN 13: 9783319208275
Verlag: Birkhäuser, 2015

Inhaltsangabe

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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Über die Autorin bzw. den Autor

Filippo Santambrogio is currently professor at Université Claude Bernard Lyon 1, after having completed his studies in Pisa and starting his career in Paris. He is a specialist of the calculus of variations and in particular optimal transport, mean field games, and gradient flows.

Von der hinteren Coverseite

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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Verlag
Birkhäuser
Erscheinungsdatum
2015
Sprache
Englisch
ISBN 10 
3319208276
ISBN 13 
9783319208275
Einband
Gebundene Ausgabe
Auflage
1
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