Optimal Transportation and Action-Minimizing Measures

Released on by Alessio Figalli
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  • Optimal Transportation and Action-Minimizing Measures Book Detail

  • Author : Alessio Figalli
  • Release Date : 2008-07-17
  • Publisher : Edizioni della Normale
  • Genre : Mathematics
  • Pages : 0
  • ISBN 13 : 9788876423307
  • File Size : 45,45 MB
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Optimal Transportation and Action-Minimizing Measures by Alessio Figalli PDF Summary

Book Description: 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.

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