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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)
MathSciNet review: 1464149
MSC: Primary 35Q99; Secondary 49J10

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Table of Contents


  • 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