Optimal Transport for Applied Mathematicians - Filippo Santambrogio

Optimal Transport for Applied Mathematicians

Calculus of Variations, PDEs, and Modeling
Buch | Hardcover
XXVII, 353 Seiten
2015 | 1st ed. 2015
Springer International Publishing (Verlag)
978-3-319-20827-5 (ISBN)
64,19 inkl. MwSt
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.

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 book offers an excellent, exciting and enjoyable, tour through the theory of optimal transportation, with a very good choice of topics ... . It is well written and thorough and provides an excellent introduction to applied mathematicians ... . a carefully selected list of exercises, make it ideal either as a textbook for an advanced postgraduate of doctoral level course, or for independent study." (Athanasios Yannacopoulos, zbMATH 1401.49002, 2019)

"This book is very well written, and the proofs are carefully chosen and adapted. It is suitable for the researcher or the student willing to enter this field as well as for the professor planning a course on this topic. Thanks to the discussions at the end of each chapter and to the rich bibliography it is also a very good reference book." (Luigi De Pascale, Mathematical Reviews, January, 2017)

Erscheint lt. Verlag 27.10.2015
Reihe/Serie Progress in Nonlinear Differential Equations and Their Applications
Zusatzinfo XXVII, 353 p.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Gewicht 843 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Angewandte Mathematik
Schlagworte fluid mechanics • Fokker-Planck Equation • Gradient flows • measure theory • Monge-Ampère equation • optimal transport • Ordinary differential equations • Partial differential equations
ISBN-10 3-319-20827-6 / 3319208276
ISBN-13 978-3-319-20827-5 / 9783319208275
Zustand Neuware
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