Gradient Flows In Metric Spaces and in the Space of Probability Measures
This book is devoted to a theory of gradient ?ows in spaces which are not nec- sarily endowed with a natural linear or di?erentiable structure. It is made of two parts, the ?rst one concerning gradient ?ows in metric spaces and the second one 2 1 devoted to gradient ?ows in the L -Wasserstein space...
| Main Authors: | , , |
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| Format: | eBook |
| Language: | English |
| Published: |
Basel
Birkhäuser
2005, 2005
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| Edition: | 1st ed. 2005 |
| 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:
- 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
- Notation
- 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 Pp(X) and the Continuity Equation
- Convex Functionals in Pp(X)
- Metric Slope and Subdifferential Calculus in Pp(X)
- Gradient Flows and Curves of Maximal Slope in Pp(X)