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Gradient Flows: In Metric Spaces and in the Space of Probability Measures

Luigi Ambrosio, Nicola Gigli, and Giuseppe Savaré
Publisher: 
Birkhäuser
Publication Date: 
2005
Number of Pages: 
33
Format: 
Paperback
Series: 
Lectures in Mathematics
Price: 
59.95
ISBN: 
3-7643-2428-7
Category: 
Monograph
We do not plan to review this book.

 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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