Siberian Mathematical Journal

, Volume 11, Issue 5, pp 833–846 | Cite as

On stability bounds in the liouville theorem on conformal mappings of multidimensional spaces

  • Yu. G. Reshetnyak


Conformal Mapping Stability Bound Multidimensional Space Liouville Theorem 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    M. A. Lavrent'ev, “Stability in the Liouville theorem,” Dokl. Akad. Nauk SSSR,95, 925–926 (1954).Google Scholar
  2. 2.
    M. A. Lavrent'ev, “Quasi-conformal mappings,” Tr. III Vsesoyuzn. Matem. S'ezda, Vol.3, Obzornye Doklady (1958), pp. 198–208.Google Scholar
  3. 3.
    Yu. G. Reshetnyak, “On stability of conformal mappings in multidimensional spaces,” Sibirsk. Matem. Zh.,8, No. 1, 111–134 (1967).Google Scholar
  4. 4.
    Yu. G. Reshetnyak, “Stability theorems for mappings of bounded distortion,” Sibirsk. Matem. Zh.,9, No. 3, 667–684 (1968).Google Scholar
  5. 5.
    Yu. G. Reshetnyak, “Bounds for certain differential operators with finite dimensional kernel,” Sibirsk. Matem. Zh.,11, No. 2 (1970).Google Scholar
  6. 6.
    N. N. Ural'tseva, “Bounds for a modulus of continuity of the first derivatives for a class of elliptic differential equations,” Tr. Matem. Seminara LOMI (1968).Google Scholar
  7. 7.
    S. L. Sobolev, On Some Applications of Functional Analysis to Mathematical Physics [in Russian], Vol. 1, Izd. LGU (1950).Google Scholar
  8. 8.
    A. I. Koshelev, “On boundedness in Lp of derivatives of solutions of elliptic differential equations,” Matem. Sb.,38, No. 3, 359–372 (1956).Google Scholar
  9. 9.
    B. A. Rozenfel'd, Non-Euclidean Geometry [in Russian], Izd. Akad. Nauk SSSR, Moscow (1955).Google Scholar
  10. 10.
    Yu. G. Reshetnyak, “On extremal properties of mappings with bounded distortion,” Sibirsk. Matem. Zh.,10, No. 6, 1300–1310 (1969).Google Scholar
  11. 11.
    S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press (1963).Google Scholar

Copyright information

© Consultants Bureau 1971

Authors and Affiliations

  • Yu. G. Reshetnyak

There are no affiliations available

Personalised recommendations