Skip to main content
Log in

On variations for mappings with restrictions on dilation in measure

  • Brief Communication
  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We construct variations for classes of homeomorphisms with generalized derivatives in the case where restrictions in measure of general form are imposed on large values of dilation. We use the method for the construction of variations suggested by Gutlyanskii.

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. G. David, “Solutions de l’equation de Beltrami avec ||μ||=1,”Ann. Acad. Sci. Fenn. Ser. A. I. Math.,13, 25–70 (1988).

    MATH  MathSciNet  Google Scholar 

  2. P. Tukia, “Compactness properties of μ-homeomorphisms,”Ann. Acad. Sci. Fenn. Ser. A. I. Math.,16, 47–69 (1991).

    MathSciNet  Google Scholar 

  3. V. L. Potemkin and V. I. Ryazanov, “On homeomorphisms of Sobolev class with restrictions on dilation in measure,”Dokl. Akad. Nauk Ukrainy, No. 7, 15–19 (1995).

    Google Scholar 

  4. V. Ya. Gutlyanskii, “On a method of variations for schlicht analytic functions with quasiconformal extension,”Sib. Mat. Zk,21, No. 2, 61–78 (1980).

    MathSciNet  Google Scholar 

  5. 0. Lehto and K. Virtanen,Quasikonforme Abbildungen, Springer, Berlin 1965.

    MATH  Google Scholar 

  6. N. Dunford and J. T. Schwartz,Linear Operators. General Theory [Russian translation], Inostrannaya Literature, Moscow (1962).

    Google Scholar 

  7. V. I. Ryazanov, “On quasiconformal mappings with restrictions in measure,”Ukr. Mat. Zk,45, No. 7, 1009–1019 (1993).

    MathSciNet  Google Scholar 

  8. L. Ahlfors,Lectures on Quasiconformal Mappings [Russian translation], Mir, Moscow 1969.

    MATH  Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Potemkin, V.L. On variations for mappings with restrictions on dilation in measure. Ukr Math J 48, 801–804 (1996). https://doi.org/10.1007/BF02384230

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02384230

Keywords

Navigation