Gradient Flows

1. Introduction

2. Notation

Part I. Gradient Flow in Metric Spaces

3. Curves and Gradients in Metric Spaces

4. Existence of Curves of Maximal Slope and their Variational Approximation

5. Proofs of the Convergence Theorems

6. Uniqueness, Generation of Contraction Semigroups, Error Estimates

Part II. Gradient Flow in the Space of Probability Measures

7. Preliminary Results on Measure Theory

8. The Optimal Transportation Problem

9. The Wasserstein Distance and its Behaviour along Geodesics

10. Absolutely Continuous Curves in p(X) and the Continuity Equation

11. Convex Functionals in p(X)

12. Metric Slope and Subdifferential Calculus in (X)

13. Gradient Flows and Curves of Maximal Slope in p(X)

14. Appendix

Keywords: MATHEMATICS / General MAT000000