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Siberian Mathematical Journal

, Volume 35, Issue 4, pp 766–782 | Cite as

On stability of isometric transformations

  • Yu. G. Reshetnyak
Article

Keywords

Isometric Transformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    F. W. Gehring, “Rings and quasiconformal mappings in space,” Trans. Amer. Math. Soc.,103, 353–393 (1962).Google Scholar
  2. 2.
    Yu. G. Reshetnyak, “Liouville's theorem on conformal mappings under minimal hypotheses on smoothness,” Sibirsk. Mat. Zh.,84, No. 4, 835–840 (1967).Google Scholar
  3. 3.
    B. V. Boyarsky and T. Iwaniec, “Another approach to Liouville's theorem,” Math. Nachr.,107, 253–262 (1982).Google Scholar
  4. 4.
    F. John, “Rotation and strain,” Comm. Pure Appl. Math.,14, No. 3, 391–413 (1961).Google Scholar
  5. 5.
    D. A. Trotsenko, “Properties of domains with nonsmooth boundary,” Sibirsk. Mat. Zh.,22, No. 4, 221–224 (1981).Google Scholar
  6. 6.
    L. G. Gurov and Yu. G. Reshetnyak, “On an analog of the concept of function with bounded mean oscillation,” Sibirsk. Mat. Zh.,17, No. 3, 540–546 (1976).Google Scholar
  7. 7.
    Yu. G. Reshetnyak, “Stability estimates in Liouville's theorem andL p-integrability of the derivatives of quasiconformal mappings,” Sibirsk. Mat. Zh.,17, No. 4, 868–896 (1976).Google Scholar
  8. 8.
    Yu. G. Reshetnyak, “Estimates in the classW p1 for stability in Liouville's theorem on conformal mappings for a closed domain,” Sibirsk. Mat. Zh.,17, No. 6, 1382–1394 (1976).Google Scholar
  9. 9.
    Yu. G. Reshetnyak, Stability Theorems in Geometry and Analysis [in Russian], Nauka, Novosibirsk (1982).Google Scholar
  10. 10.
    S. L. Sobolev, Some Applications of Functional Analysis to Mathematical Physics [in Russian], Nauka, Moscow (1988).Google Scholar
  11. 11.
    O. V. Besov, B. P. Il'in, and S. M. Nikol'skii, Integral Representations of Functions and Embedding Theorems [in Russian], Nauka, Moscow (1975).Google Scholar
  12. 12.
    V. M. Gol'dshtein and Yu. G. Reshetnyak, Quasiconformal Mappings and Sobolev Spaces, Kluwer Akad. Publ., Dordrecht-Boston-London (1990).Google Scholar
  13. 13.
    Yu. G. Reshetnyak, “General theorems on semicontinuity and convergence with a functional,” Sibirsk. Mat. Zh.,8, No. 5, 1051–1069 (1967).Google Scholar
  14. 14.
    Yu. G. Reshetnyak, Space Mappings with Bounded Distortion, Amer. Math. Soc., Providence (1989).Google Scholar
  15. 15.
    Yu. G. Reshetnyak, “Stability theorems for mappings with bounded distortion,” Sibirsk. Mat. Zh.,9, No. 3, 667–684 (1968).Google Scholar
  16. 16.
    F. John and L. Nirenberg, “On functions of bounded mean oscillation,” Comm. Pure Appl. Math.,14, No. 3, 415–426 (1961).Google Scholar
  17. 17.
    Yu. G. Reshetnyak, “Estimates for certain differential operators with finite-dimensional kernel,” Sibirsk. Mat. Zh.,11, No. 3, 903–917 (1970).Google Scholar
  18. 18.
    E. M. Stein, Singular Integrals and Differentiability Properties of Functions [Russian translation], Mir, Moscow (1973).Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • Yu. G. Reshetnyak
    • 1
  1. 1.Novosibirsk

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