Chapter

Optimal Transportation and Applications

Volume 1813 of the series Lecture Notes in Mathematics pp 123-160

Date:

Existence and stability results in the L1 theory of optimal transportation

  • Luigi AmbrosioAffiliated withScuola Normale Superiore Email author 
  • , Aldo PratelliAffiliated withScuola Normale Superiore

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Contents.

  • 1 Introduction

  • 2 Notation

  • 3 Duality and optimality conditions

  • 4 \(\Gamma \)-convergence and \(\Gamma \)-asymptotic expansions

  • 5 1-dimensional theory

  • 6 Transport rays and transport set

  • 7 A stability result

  • 8 A counterexample

  • 9 Appendix: disintegration of measures

  • References

Mathematics Subject Classification (2000):

35J20 35J70 35K65 35L70 35Q60 35Q75 49K20 49K99 60F99 52A99 74P99 82C70 82C99