Authors:
Gives for the first time a generalized approach to many problems of different nature, in the context of optimal transportation
Part of the book series: Publications of the Scuola Normale Superiore (PSNS, volume 8)
Part of the book sub series: Theses (Scuola Normale Superiore) (TSNS)
About this book
In this book we describe recent developments in the theory of optimal transportation, and some of its applications to fluid dynamics. Moreover we explore new variants of the original problem, and we try to figure out some common (and sometimes unexpected) features in this emerging variety of problems .
In Chapter 1 we study the optimal transportation problem on manifolds with geometric costs coming from Tonelli Lagrangians, while in Chapter 2 we consider a generalization of the classical transportation problem called the optimal irrigation problem. Then, Chapter 3 is about the Brenier variational theory of incompressible flows, which concerns a weak formulation of the Euler equations viewed as a geodesic equation in the space of measure-preserving diffeomorphism. Chapter 4 is devoted to the study of regularity and uniqueness of solutions of Hamilton-Jacobi equations applying the Aubry-Mather theory. Finally, the last chapter deals with a DiPerna-Lions theory for martingale solutions of stochastic differential equations.
Keywords
- Euler equation
- Hamilton-Jacobi equation
- irrigation problem
- optimal transport
- partial differential equations
Authors and Affiliations
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Labo. J.-A. Dieudonne, Université Nice CNRS UMR 6621, Vice CX, France
Alessio Figalli
Bibliographic Information
Book Title: Optimal Transportation and Action-Minimizing Measures
Authors: Alessio Figalli
Series Title: Publications of the Scuola Normale Superiore
Publisher: Edizioni della Normale Pisa
Copyright Information: Edizioni della Normale 2008
Series ISSN: 2239-1460
Series E-ISSN: 2532-1668
Edition Number: 1
Number of Pages: XIX, 254
Topics: Calculus of Variations and Optimization, Differential Equations