Francesco Maggi (Austin University of Texas)

Optimal Mass Transport on Euclidean Spaces

• Gebundenes Buch

Produktbeschreibung

This is a graduate-level introduction to the key ideas and theoretical foundation of the vibrant field of optimal mass transport in the Euclidean setting. Taking a pedagogical approach, it introduces concepts gradually and in an accessible way, while also remaining technically and conceptually complete.

Produktdetails

• Cambridge Studies in Advanced Mathematics
• Verlag: Cambridge University Press
• Seitenzahl: 345
• Erscheinungstermin: 16. November 2023
• Englisch
• Abmessung: 229mm x 152mm x 22mm
• Gewicht: 622g
• ISBN-13: 9781009179706
• ISBN-10: 1009179705
• Artikelnr.: 67744152

Autorenporträt

Francesco Maggi is Professor of Mathematics at the University of Texas at Austin. His research interests include the calculus of variations, partial differential equations, and optimal mass transport. He is the author of Sets of Finite Perimeter and Geometric Variational Problems published by Cambridge University Press.

Inhaltsangabe

Preface
Notation
Part I. The Kantorovich Problem: 1. An introduction to the Monge problem
2. Discrete transport problems
3. 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: 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: 16. Optimal transport maps on the real line
17. Disintegration
18. Solution to the Monge problem with linear cost
19. An introduction to the needle decomposition method
Appendix A: Radon measures on Rn and related topics
Appendix B: Bibliographical Notes
Bibliography
Index.