Gradient Flows
In Metric Spaces and in the Space of Probability Measures
1st Edition
Published in July 2004
Book
Paperback/Softback
VII, 333 pages
978-3-7643-2428-5 (ISBN)
Description
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 probability measures on a separable Hilbert space, endowed with the Kantorovich-Rubinstein-Wasserstein distance.
The two parts have some connections, due to the fact that the space of probability measures provides an important model to which the "metric" theory applies, but the book is conceived in such a way that the two parts can be read independently, the first one by the reader more interested in non-smooth analysis and analysis in metric spaces, and the second one by the reader more orientated towards the applications in partial differential equations, measure theory and probability.
The two parts have some connections, due to the fact that the space of probability measures provides an important model to which the "metric" theory applies, but the book is conceived in such a way that the two parts can be read independently, the first one by the reader more interested in non-smooth analysis and analysis in metric spaces, and the second one by the reader more orientated towards the applications in partial differential equations, measure theory and probability.
More details
Other editions
New editions
Luigi Ambrosio | Nicola Gigli | Giuseppe Savare
Gradient Flows
In Metric Spaces and in the Space of Probability Measures
Book
03/2008
2nd Edition
Birkhäuser
€128.39
Shipment within 10-15 days
Additional editions
Luigi Ambrosio | Nicola Gigli | Giuseppe Savare
Gradient Flows
In Metric Spaces and in the Space of Probability Measures
E-Book
03/2006
1st Edition
Birkhäuser
€36.99
Available for download
Content
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.