Gradient Flows

in Metric Spaces and in the Space of Probability Measures

Authors:

ISBN: 978-3-7643-8721-1 (Print) 978-3-7643-8722-8 (Online)

Table of contents (14 chapters)

  1. Front Matter

    Pages i-ix

  2. Introduction

    1. No Access

      Book Chapter

      Pages 1-17

      Introduction

  3. Notation

    1. No Access

      Book Chapter

      Pages 18-19

      Notation

  4. Gradient Flow in Metric Spaces

    1. Front Matter

      Pages 21-21

    2. No Access

      Book Chapter

      Pages 23-37

      Curves and Gradients in Metric Spaces

    3. No Access

      Book Chapter

      Pages 39-57

      Existence of Curves of Maximal Slope and their Variational Approximation

    4. No Access

      Book Chapter

      Pages 59-74

      Proofs of the Convergence Theorems

    5. No Access

      Book Chapter

      Pages 75-102

      Uniqueness, Generation of Contraction Semigroups, Error Estimates

  5. Gradient Flow in the Space of Probability Measures

    1. Front Matter

      Pages 103-103

    2. No Access

      Book Chapter

      Pages 105-131

      Preliminary Results on Measure Theory

    3. No Access

      Book Chapter

      Pages 133-150

      The Optimal Transportation Problem

    4. No Access

      Book Chapter

      Pages 151-165

      The Wasserstein Distance and its Behaviour along Geodesics

    5. No Access

      Book Chapter

      Pages 167-200

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

    6. No Access

      Book Chapter

      Pages 201-225

      Convex Functionals in p (X)

    7. No Access

      Book Chapter

      Pages 227-278

      Metric Slope and Subdifferential Calculus in (X)

    8. No Access

      Book Chapter

      Pages 279-306

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

    9. No Access

      Book Chapter

      Pages 307-319

      Appendix

  6. Back Matter

    Pages 321-334