Gradient Flows in Metric Spaces and in the Space of Probability Measures /
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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| Other Authors: | , |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Basel :
Birkhäuser Basel,
2008.
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| Edition: | Second Edition. |
| Series: | Lectures in mathematics ETH Zürich.
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| Subjects: | |
| Online Access: | Access E-Book Full text (Wentworth users only). |
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.