Gradient Flows In Metric Spaces and in the Space of Probability Measures
Main Authors: | , , |
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Format: | eBook |
Language: | English |
Published: |
Basel
Birkhäuser
2008, 2008
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Edition: | 2nd ed. 2008 |
Series: | Lectures in Mathematics. ETH Zürich
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Subjects: | |
Online Access: | |
Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- Notation
- Notation
- Gradient Flow in Metric Spaces
- Curves and Gradients in Metric Spaces
- Existence of Curves of Maximal Slope and their Variational Approximation
- Proofs of the Convergence Theorems
- Uniqueness, Generation of Contraction Semigroups, Error Estimates
- Gradient Flow in the Space of Probability Measures
- Preliminary Results on Measure Theory
- The Optimal Transportation Problem
- The Wasserstein Distance and its Behaviour along Geodesics
- Absolutely Continuous Curves in p(X) and the Continuity Equation
- Convex Functionals in p(X)
- Metric Slope and Subdifferential Calculus in (X)
- Gradient Flows and Curves of Maximal Slope in p(X)