Contents
1. Introduction 1
2. Uniform estimates on the p-Laplacian, limits as p —» oo ... 7
3. The transport set and transport rays 16
4. Differentiability and smoothness properties of the potential 22
5. Generic properties of transport rays 28
6. Behavior of the transport density along rays 36
7. Vanishing of the transport density at the ends of rays 44
8. Approximate mass transfer plans 52
9. Passage to limits a.e 56
10. Optimally 62
Appendix: Approximating semiconcave and semiconvex functions by
C2
functions .. 63
Bibliography 65
vii
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