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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: https://doi.org/10.1090/memo/0653
MathSciNet review: 1464149
MSC: Primary 35Q99; Secondary 49J10

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Table of Contents

Chapters

• 1. Introduction
• 2. Uniform estimates on the $p$-Laplacian, limits as $p \to \infty$
• 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