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Optimal Transport for Applied Mathematicians = Calculus of Variations, PDEs, and Modeling /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Optimal Transport for Applied Mathematicians/ by Filippo Santambrogio.
其他題名:	Calculus of Variations, PDEs, and Modeling /
作者:	Santambrogio, Filippo.
面頁冊數:	XXVII, 353 p. 30 illus., 19 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Calculus of variations. -
電子資源:	https://doi.org/10.1007/978-3-319-20828-2
ISBN:	9783319208282

Optimal Transport for Applied Mathematicians = Calculus of Variations, PDEs, and Modeling /
Santambrogio, Filippo.

Optimal Transport for Applied MathematiciansCalculus of Variations, PDEs, and Modeling /[electronic resource] :by Filippo Santambrogio. - 1st ed. 2015. - XXVII, 353 p. 30 illus., 19 illus. in color.online resource. - Progress in Nonlinear Differential Equations and Their Applications,871421-1750 ;. - Progress in Nonlinear Differential Equations and Their Applications,87.

Preface -- Primal and Dual Problems -- One-Dimensional Issues -- L^1 and L^infinity Theory -- Minimal Flows -- Wasserstein Spaces -- Numerical Methods -- Functionals over Probabilities -- Gradient Flows -- Exercises -- References -- Index. .

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.

ISBN: 9783319208282

Standard No.: 10.1007/978-3-319-20828-2doiSubjects--Topical Terms:

527927
Calculus of variations.

LC Class. No.: QA315-316

Dewey Class. No.: 515.64

Optimal Transport for Applied Mathematicians = Calculus of Variations, PDEs, and Modeling /
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