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Gradient Flows : in Metric Spaces and in the Space of Probability Measures

Overview of attention for book
Cover of 'Gradient Flows : in Metric Spaces and in the Space of Probability Measures'

Table of Contents

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    Book Overview
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    Chapter 1 Introduction
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    Chapter 2 Notation
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    Chapter 3 Curves and Gradients in Metric Spaces
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    Chapter 4 Existence of Curves of Maximal Slope and their Variational Approximation
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    Chapter 5 Proofs of the Convergence Theorems
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    Chapter 6 Uniqueness, Generation of Contraction Semigroups, Error Estimates
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    Chapter 7 Preliminary Results on Measure Theory
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    Chapter 8 The Optimal Transportation Problem
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    Chapter 9 The Wasserstein Distance and its Behaviour along Geodesics
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    Chapter 10 Absolutely Continuous Curves in P p ( X ) and the Continuity Equation
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    Chapter 11 Convex Functionals in P p ( X )
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    Chapter 12 Metric Slope and Subdifferential Calculus in P p ( X )
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    Chapter 13 Gradient Flows and Curves of Maximal Slope in P p ( X )
Attention for Chapter 10: Absolutely Continuous Curves in P p ( X ) and the Continuity Equation
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