Articoli correlati a Optimal transportation and action. Minimizing measures:...
Sinossi
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.
Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.
Contenuti
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.
Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.
- EditoreScuola Normale Superiore
- Data di pubblicazione2008
- ISBN 10 8876423303
- ISBN 13 9788876423307
- RilegaturaCopertina flessibile
- LinguaInglese
- Numero edizione1
- Numero di pagine251
- Contatto del produttorenon disponibile
(nessuna copia disponibile)
Cerca: Inserisci un desiderataNon riesci a trovare il libro che stai cercando? Continueremo a cercarlo per te. Se uno dei nostri librai lo aggiunge ad AbeBooks, ti invieremo una notifica!
Inserisci un desiderata