Progress in Nonlinear Differential Equations and Their Applications: Calculus of Variations, PDEs, and Modeling

Santambrogio, Filippo

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.

Details

Published by: Birkhäuser

Publication Date: 2015-10-27

Format: Hardcover

ISBN-13: 9783319208275

DOI: 10.1007/978-3-319-20828-2

Dimensions: 235cm x155cm

Pages: 353