Skip to main content
Log in

Stability estimates in Liouville's theorem and the Lp-integrability of the derivatives of quasi-conformal mappings

  • Published:
Siberian Mathematical Journal 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.

Literature Cited

  1. M. A. Lavrent'ev, “On stability in Liouville's theorem,” Dokl. Akad. Nauk SSSR,95, No. 5, 925–926 (1954).

    Google Scholar 

  2. M. A. Lavrent'ev, “Quasi-conformal mappings,” Proceedings of the Third All-Union Mathematical Congree, Vol. 3, Survey Reports [in Russian], Izd-vo Akad. Nauk SSSR, Moscow (1958), pp. 198–208.

    Google Scholar 

  3. Yu. G. Reshetnyak, “Stability in Liouville's theorem on conformal mappings,” in: Some Problems of Mathematics and Mechanics (On the 60th birthday of the Academician M. A. Lavrent'ev) [in Russian], Izd. SO AN SSSR, Novosibirsk (1961), pp. 219–223.

    Google Scholar 

  4. P. P. Belinskii, “Stability in Liouville's theorem on conformal mappings in space,” in: Some Problems of Mathematics and Mechanics (On the 70th birthday of the Academician M. A. Lavrent'ev) [in Russian], Nauka, Leningrad (1971), pp. 88–101.

    Google Scholar 

  5. Yu. G. Reshetnyak, “A stability estimate in Liouville's theorem on conformal mappings of multidimensional spaces,” Sibirsk. Matem. Zh.,11, No. 5, 1121–1139 (1970).

    Google Scholar 

  6. P. P. Belinskii, “The order of closeness of a spatial conformal mapping to a conformal mapping,” Sibirsk. Matem. Zh.,14, No. 3, 475–483 (1973).

    Google Scholar 

  7. S. L. Sobolev, Some Applications of Functional Analysis in Mathematical Physics [in Russian], Izd. Leningr. Un-ta, Leningrad (1950).

    Google Scholar 

  8. F. W. Gehring, “The Lp-integrability of the partial derivatives of a quasi-conformal mapping,” Acta Math.,130, 265–277 (1973).

    Google Scholar 

  9. Yu. G. Reshetnyak, “Estimates for some differential operators with a finite-dimensional kernel,” Sibirsk. Matem. Zh.,11, No. 2, 414–428 (1970).

    Google Scholar 

  10. L. G. Gurov and Yu. G. Reshetnyak, “An analog of the concept of a function with bounded mean oscillation,” Sibirsk. Matem. Zh.,17, No. 3, 540–546 (1976).

    Google Scholar 

  11. F. John and L. Nirenberg, “On functions of bounded mean oscillation,” Communs. Pure and Appl. Math.,14, No. 3, 415–426 (1961).

    Google Scholar 

  12. Yu. G. Reshetnyak, “Stability in Liouville's theorem on conformal mappings for domains with a nonsmooth boundary,” Sibirsk. Matem. Zh.,17, No. 2, 361–369 (1976).

    Google Scholar 

  13. S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, New York (1962).

    Google Scholar 

  14. Yu. G. Reshetnyak, “Mappings with bounded distortion as extremals of integrals of Dirichlet type,” Sibirsk. Matem. Zh.,9, No. 3, 652–666 (1968).

    Google Scholar 

  15. Yu. G. Reshetnyak, “Stability theorems for mappings with bounded distortion,” Sibirsk. Matem. Zh.,9, No. 3, 667–685 (1968).

    Google Scholar 

  16. Yu. G. Reshetnyak, “General theorems on semicontinuity and convergence for a functional,” Sibirsk. Matem. Zh.,8, No. 5, 1051–1069 (1967).

    Google Scholar 

Download references

Authors

Additional information

Translated from Sibirskii Matematicheskii Zhurnal, Vol. 17, No. 4, pp. 868–896, July–August, 1976.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Reshetnyak, Y.G. Stability estimates in Liouville's theorem and the Lp-integrability of the derivatives of quasi-conformal mappings. Sib Math J 17, 653–674 (1976). https://doi.org/10.1007/BF00971676

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00971676

Keywords

Navigation