Skip to main content
Log in

The Kantorovich Problem with a Parameter and Density Constraints

  • Short Communications
  • Published:
Mathematical Notes Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. L. Ambrosio and N. Gigli, in Lecture Notes in Math., Vol. 2062: Modelling and Optimisation of Flows on Networks (Springer, Heidelberg, 2013), pp. 1–155.

    Google Scholar 

  2. V. I. Bogachev and A. V. Kolesnikov, Russian Math. Surveys 67 (5), 785 (2012).

    Article  MathSciNet  Google Scholar 

  3. C. Villani, Grundlehren Math. Wiss., Vol. 338: Optimal Transport. Old and New (Springer- Verlag, Berlin, 2009).

    Google Scholar 

  4. J. Korman and R. J. McCann, Trans. Amer. Math. Soc. 367 (3), 1501 (2015).

    Article  MathSciNet  Google Scholar 

  5. A. N. Doledenok, Math. Notes 104 (1), 39 (2018).

    Article  MathSciNet  Google Scholar 

  6. V. I. Bogachev and I. I. Malofeev, Dokl. Math. 100 (1), 349 (2019).

    Article  Google Scholar 

  7. V. I. Bogachev and I. I. Malofeev, J. Math. Anal. Appl. 486 (1, no. 123883) (2020).

    Article  Google Scholar 

  8. V. I. Bogachev, Measure Theory (Springer- Verlag, Berlin, 2007), Vol. I, II.

    Book  Google Scholar 

  9. C. Castaing and M. Valadier, Lecture Notes in Math., Vol. 580: Convex Analysis and Measurable Multifunctions (Springer- Verlag, Berlin, 1977).

    Book  Google Scholar 

  10. T. V. Bogachev and S. N. Popova, Math. Notes 109 (2), 163 (2021).

    Article  Google Scholar 

  11. V. I. Bogachev, Math. Surveys Monogr., Vol. 234: Weak Convergence of Measures (Amer. Math. Soc., Providence, RI, 2018), Vol. 234.

    Book  Google Scholar 

  12. V. I. Bogachev, Math. Notes 110 (3), 449 (2021).

    Article  Google Scholar 

Download references

Funding

This work was supported by the Russian Foundation for Basic Research under grant 20-01-00432 of the Moscow Center of Fundamental and Applied Mathematics, and by the “Basis” Foundation under grant 18-1-6-83-1. The first author was supported by the Simons-IUM Fellowship.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. I. Bogachev.

Additional information

Translated from Matematicheskie Zametki, 2021, Vol. 110, pp. 922–926 https://doi.org/10.4213/mzm13187.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bogachev, V.I., Doledenok, A.N. & Malofeev, I.I. The Kantorovich Problem with a Parameter and Density Constraints. Math Notes 110, 952–955 (2021). https://doi.org/10.1134/S0001434621110328

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0001434621110328

Keywords

Navigation