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Optimal transportation and action-minimizing measures

Author: Alessio Figalli
Publisher: Pisa : Ed. della normale, impr. 2008.
Dissertation: Texte remanié de: Thèse de doctorat: Mathématiques: Lyon, École normale supérieure (sciences): 2007.
Edition/Format:   Thesis/dissertation : Thesis/dissertation : EnglishView all editions and formats
Database:WorldCat
Summary:

This book describes recent developments in the theory of optimal transportation, and some of its applications to fluid dynamics. It also explores new variants of the original problem and examines  Read more...

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Material Type: Thesis/dissertation, Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Alessio Figalli
ISBN: 9788876423307 8876423303
OCLC Number: 494080346
Description: 1 v. (XIX-254 p.) ; 30 cm
Contents: 1. The optimal transportation problem - Optimal transportation on non-compact manifolds, costs obtained from Lagrangians, interpolation and absolute continuity, displacement convexity.- 2. The irrigation problem - Dynamic cost on traffic plans, syncronization, stability.- 3. Variational models for the incompressible Euler equations - Arnold's least action problem, Brenier's variationals models, gap phenomena, necessary and sufficient optimality conditions, regularity of the pressure.- 4. On the structure of the Aubry set and Hamilton-Jacobi equation - Structure of the Mather quotient set, estimate of its Hausdorff dimensions, applications in dynamics.
Responsibility: Alessio Figalli.
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