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 Pp(X) and the Continuity Equation
11. Convex Functionals in Pp(X)
12. Metric Slope and Subdifferential Calculus in Pp(X)
13. Gradient Flows and Curves of Maximal Slope in Pp(X)

DRM-restrictions

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Avainsanat: MATHEMATICS / General MAT000000