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
- 4 The Brenier Theorem
- 5 First Order Differentiability of Convex Functions
- 6 The Brenier–McCann Theorem
- 7 Second Order Differentiability of Convex Functions
- 8 The Monge–Ampère Equation for Brenier Maps
- Part III Applications to PDE and the Calculus of Variations and the Wasserstein Space
- 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
7 - Second Order Differentiability of Convex Functions
from Part II - Solution of the Monge Problem with Quadratic Cost: The Brenier–McCann Theorem
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
- 4 The Brenier Theorem
- 5 First Order Differentiability of Convex Functions
- 6 The Brenier–McCann Theorem
- 7 Second Order Differentiability of Convex Functions
- 8 The Monge–Ampère Equation for Brenier Maps
- Part III Applications to PDE and the Calculus of Variations and the Wasserstein Space
- 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
Fine second-order differentiability properties of convex functions.
- Type
- Chapter
- Information
- Optimal Mass Transport on Euclidean Spaces , pp. 77 - 85Publisher: Cambridge University PressPrint publication year: 2023