# Differential equations methods for the Monge-Kantorovich mass transfer problem

### About this Title

**L. C. Evans** and **W. Gangbo**

Publication: Memoirs of the American Mathematical Society

Publication Year
1999: Volume 137, Number 653

ISBNs: 978-0-8218-0938-9 (print); 978-1-4704-0242-6 (online)

DOI: http://dx.doi.org/10.1090/memo/0653

MathSciNet review: 1464149

MSC (1991): Primary 35Q99; Secondary 49J10

### Table of Contents

**Chapters**

- 1. Introduction
- 2. Uniform estimates on the -Laplacian, limits as
- 3. The transport set and transport rays
- 4. Differentiability and smoothness properties of the potential
- 5. Generic properties of transport rays
- 6. Behavior of the transport density along rays
- 7. Vanishing of the transport density at the ends of rays
- 8. Approximate mass transfer plans
- 9. Passage to limits a.e.
- 10. Optimality