Mathematical Aspects of Evolving Interfaces pp 1-52

Part of the Lecture Notes in Mathematics book series (LNM, volume 1812)

Lecture Notes on Optimal Transport Problems

Chapter

Abstract

  • 1 Some elementary examples

  • 2 Optimal transport plans: existence and regularity

  • 3 The one dimensional case

  • 4 The ODE version of the optimal transport problem

  • 5 The PDE version of the optimal transport problem and the p-laplacian approximation

  • 6 Existence of optimal transport maps

  • 7 Regularity and uniqueness of the transport density

  • 8 The Bouchitté-Buttazzo mass optimization problem

  • 9 Appendix: some measure theoretic results

  • References

Mathematics Subject Classification (2000):

35-02 35Bxx 35QXX 35K57 53C44 76D05 80A22 

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Copyright information

© Springer-Verlag Berlin/Heidelberg 2003

Authors and Affiliations

  1. 1.Scuola Normale SuperiorePisaItaly

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