Gradient Flows

in Metric Spaces and in the Space of Probability Measures

Authors:

ISBN: 978-3-7643-2428-5 (Print) 978-3-7643-7309-2 (Online)

Table of contents (13 chapters)

  1. Front Matter

    Pages i-vii

  2. No Access

    Chapter

    Pages 1-17

    Introduction

  3. No Access

    Chapter

    Pages 18-19

    Notation

  4. Gradient Flow in Metric Spaces

    1. No Access

      Chapter

      Pages 23-37

      Curves and Gradients in Metric Spaces

    2. No Access

      Chapter

      Pages 39-57

      Existence of Curves of Maximal Slope and their Variational Approximation

    3. No Access

      Chapter

      Pages 59-74

      Proofs of the Convergence Theorems

    4. No Access

      Chapter

      Pages 75-102

      Uniqueness, Generation of Contraction Semigroups, Error Estimates

  5. Gradient Flow in the Space of Probability Measures

    1. No Access

      Chapter

      Pages 105-131

      Preliminary Results on Measure Theory

    2. No Access

      Chapter

      Pages 133-149

      The Optimal Transportation Problem

    3. No Access

      Chapter

      Pages 151-165

      The Wasserstein Distance and its Behaviour along Geodesics

    4. No Access

      Chapter

      Pages 167-200

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

    5. No Access

      Chapter

      Pages 201-225

      Convex Functionals in P p (X)

    6. No Access

      Chapter

      Pages 227-278

      Metric Slope and Subdifferential Calculus in P p (X)

    7. No Access

      Chapter

      Pages 279-306

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

  6. Back Matter

    Pages 307-336