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Gradient flows [electronic resource] : in metric spaces and in the space of probability measures / Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré

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This book is devoted to a theory of gradient flows in spaces which are not necessarily endowed with a natural linear or differentiable structure. It consists of two parts, the first one concerning gradient flows in metric spaces and the second one devoted to gradient flows in the space of probabilit...

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Bibliographic Details
Online Access: Full Text (via Springer)
Main Author: Ambrosio, Luigi
Other Authors: Gigli, Nicola, Savaré, Giuseppe
Format: Electronic eBook
Language:English
Published: Basel ; Boston : Birkhäuser, ©2008.
Edition:2nd ed.
Series:Lectures in mathematics ETH Zürich.
Subjects:
Measure theory.
Metric spaces.
Differential equations, Partial.
Monotone operators.
Evolution equations, Nonlinear.
Table of Contents:
  • 1. Introduction
  • Part I. Gradient flow in metric spaces
  • 2. Curves and gradients in metric spaces
  • 3. Existence of curves of maximal slope
  • 4. Proofs of the convergence theorems
  • 5. Generation of contraction semigroups
  • Part II. Gradient flow in the Wasserstein spaces of probability measures
  • 6. Preliminary results on measure theory
  • 7. The optimal transportation problem
  • 8. The Wasserstein distance and its behaviour along geodesics
  • 9. A.c. curves and the continuity equation
  • 10. Convex functionals
  • 11. Metric slope and subdifferential calculus
  • 12. Gradient flows and curves of maximal slope
  • 13. Appendix
  • Bibliography.

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