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Catalogue Information
Field name	Details
Dewey Class	515.64
Title	Optimal Transport for Applied Mathematicians ([EBook]) : Calculus of Variations, PDEs, and Modeling / by Filippo Santambrogio.
Author	Santambrogio, Filippo
Other name(s)	SpringerLink (Online service)
Edition statement	1st ed. 2015.
Publication	Cham : Birkhäuser , 2015.
Physical Details	XXVII, 353 p. 30 illus., 19 illus. in color. : online resource.
Series	Progress in nonlinear differential equations and their applications 1421-1750 ; ; 87
ISBN	9783319208282
Summary Note	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.:
Contents note	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. .
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-3-319-20828-2
Links to Related Works	Subject References: Calculus of variations . Calculus of variations and optimal control; optimization . Differential equation . Mathematics . Measure and Integration . Measure theory . Ordinary differential equations . Partial differential equations . Authors: Santambrogio, Filippo . Corporate Authors: SpringerLink (Online service) . Series: Progress in nonlinear differential equations and their applications . Classification: 515.64 . 515.64 (DDC 22) .

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

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