Book contents
- Frontmatter
- Epigraph
- Dedication
- Contents
- Preface
- Notation
- Part I The Kantorovich Problem
- Part II Solution of the Monge Problem with Quadratic Cost: The Brenier–McCann Theorem
- Part III Applications to PDE and the Calculus of Variations and the Wasserstein Space
- 9 Isoperimetric and Sobolev Inequalities in Sharp Form
- 10 Displacement Convexity and Equilibrium of Gases
- 11 The Wasserstein Distance W2 on P2(Rn)
- 12 Gradient Flows and the Minimizing Movements Scheme
- 13 The Fokker–Planck Equation in the Wasserstein Space
- 14 The Euler Equations and Isochoric Projections
- 15 Action Minimization, Eulerian Velocities, and Otto's Calculus
- Part IV Solution of the Monge Problem with Linear Cost: The Sudakov Theorem
- Appendix A Radon Measures on Rn and Related Topics
- Appendix B Bibliographical Notes
- References
- Index
11 - The Wasserstein Distance W2 on P2(Rn)
from Part III - Applications to PDE and the Calculus of Variations and the Wasserstein Space
Published online by Cambridge University Press: 02 November 2023
Book contents
- Frontmatter
- Epigraph
- Dedication
- Contents
- Preface
- Notation
- Part I The Kantorovich Problem
- Part II Solution of the Monge Problem with Quadratic Cost: The Brenier–McCann Theorem
- Part III Applications to PDE and the Calculus of Variations and the Wasserstein Space
- 9 Isoperimetric and Sobolev Inequalities in Sharp Form
- 10 Displacement Convexity and Equilibrium of Gases
- 11 The Wasserstein Distance W2 on P2(Rn)
- 12 Gradient Flows and the Minimizing Movements Scheme
- 13 The Fokker–Planck Equation in the Wasserstein Space
- 14 The Euler Equations and Isochoric Projections
- 15 Action Minimization, Eulerian Velocities, and Otto's Calculus
- Part IV Solution of the Monge Problem with Linear Cost: The Sudakov Theorem
- Appendix A Radon Measures on Rn and Related Topics
- Appendix B Bibliographical Notes
- References
- Index
Summary
Introduction to and basic properties of the Wasserstein space.
- Type
- Chapter
- Information
- Optimal Mass Transport on Euclidean Spaces , pp. 118 - 128Publisher: Cambridge University PressPrint publication year: 2023