Optimal mass transport on Euclidean spaces /

Bibliographic Details
Main Author: Maggi, Francesco, 1978- (Author)
Corporate Author: Cambridge University Press
Format: eBook
Language:English
Published: Cambridge ; New York, NY : Cambridge University Press, 2023.
Series:Cambridge studies in advanced mathematics ; 207
Subjects:
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • An introduction to the Monge problem
  • Discrete transport problems
  • The Kantorovich problem
  • The Brenier theorem
  • First order differentiability of convex functions
  • The Brenier-McCann theorem
  • Second order differentiability of convex functions
  • The Monge-Ampere equation for Brenier maps
  • Isoperimetric and Sobolev inequalities in sharp form
  • Displacement convexity and equilibrium of gases
  • The Wasserstein distance W2 on P2(Rn)
  • Gradient flows and the minimizing movements scheme
  • The Fokker-Planck equation in the Wasserstein space
  • The Euler equations and isochoric projections
  • Action minimization, Eulerian velocities and Otto's calculus
  • Optimal transport maps on the real line
  • Disintegration
  • Solution to the Monge problem with linear cost
  • An introduction to the needle decomposition method.