Skip to main content
SpringerLink
Log in

Approximation of exact and closed differential forms by finite ones

  • 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

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Literature Cited

  1. S. L. Sobolev, “Density of finite functions in the space Lp(m)(En),” Sib. Mat. Zh.,4, No. 3, 673–682 (1963).

    MATH  MathSciNet  Google Scholar 

  2. J. G. Heywood, “On uniqueness questions in the theory of viscous flow,” Acta Math.,136, No. 1, 61–102 (1976).

    Article  MATH  MathSciNet  Google Scholar 

  3. O. V. Besov, “Extension of functions from Lp ℓ and Wp ℓ,” Trudy Steklov Math. Institute, Akad. Nauk SSSR,89, Part 2, 5–17 (1967).

    MATH  MathSciNet  Google Scholar 

  4. V. N. Maslennikova and M. E. Bogovskii, “On the density of finite solenoidal vector fields,” Sib. Mat. Zh.,19, No. 5, 1092–1108 (1978).

    MATH  MathSciNet  Google Scholar 

  5. V. N. Maslennikova and M. E. Bogovskii, “Sobolev spaces of solenoidal vector fields,” Sib. Mat. Zh.,22, No. 3, 91–118 (1981).

    MATH  MathSciNet  Google Scholar 

  6. V. N. Maslennikova and M. E. Bogovskii, “Approximation of potential and solenoidal vector fields,” Sib. Mat. Zh.,24, No. 5, 149–171 (1983).

    MathSciNet  Google Scholar 

  7. V. N. Maslennikova and M. E. Bogovskii, “Approximation of solenoidal and potential vector fields in Sobolev spaces and problems of mathematical physics,’ in: Partial Differential Equations [in Russian], Nauka, Novosibirsk (1986), pp. 129–137.

    Google Scholar 

  8. V. M. Gol'dshtein, V. I. Kuz'minov, and I. A. Shvedov, “Spaces dual to the spaces of differential forms,” Sib. Mat. Zh.,27, No. 1, 45–56 (1986).

    Article  MathSciNet  Google Scholar 

  9. V. M. Gol'dshtein, V. I. Kuz'minov, and I. A. Shvedov, “On a property of the de-Rahm regularization operators,” Sib. Mat. Zh.,25, No. 2, 104–111 (1984).

    Article  MathSciNet  Google Scholar 

  10. V. M. Gol'dshtein, V. I. Kuz'minov, and I. A. Shvedov, “Differential forms on Lipschitz manifolds,” Sib. Mat. Zh.,23, No. 2, 16–30 (1982).

    Article  MathSciNet  Google Scholar 

  11. I. Chavel, Eigenvalues in Riemannian Geometry, Academic Press, New York (1984).

    MATH  Google Scholar 

  12. R. Sulanke and P. Wingen, Differentialgeometrie und Faserbundel, Birkhauser Verlag, Basel (1972).

    Google Scholar 

  13. E. Michael, “Continuous, elections. II,” Ann. Math., Ser. 2,64, No. 3, 562–580 (1956).

    Article  MATH  MathSciNet  Google Scholar 

  14. V. M. Gol'dshtein, V. I. Kuz'minov, and I. A. Shvedov, “Lp-cohomologies of Riemannian manifolds,” in: Trudy Institut Matematiki, Siberian Branch, Acad. Sci. of the USSR,7, Issled. Geom. Matemat. Anal., Nauka, Novosibirsk (1987), pp. 101–116.

    Google Scholar 

  15. V. M. Gol'dshtein, V. I. Kuz'minov, and I. A. Shvedov, “Reduced Lp-cohomologies of distorted cylinders,” Sib. Mat. Zh.,31, No. 5, 10–23 (1990).

    MathSciNet  Google Scholar 

  16. V. M. Gol'dshtein, V. I. Kuz'minov, and I. A. Shvedov, “On the Künneth formula for Lp-cohomologies of distorted products,” Sib. Mat. Zh.,32, No. 5, 29–42 (1991).

    MathSciNet  Google Scholar 

Download references

Authors
  1. V. M. Gol'dshtein
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. I. Kuz'minov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. I. A. Shvedov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Institute of Mathematics, Siberian Branch, Academy of Sciences of the USSR, Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 33, No. 2, pp. 49–65, March–April, 1992.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gol'dshtein, V.M., Kuz'minov, V.I. & Shvedov, I.A. Approximation of exact and closed differential forms by finite ones. Sib Math J 33, 219–233 (1992). https://doi.org/10.1007/BF00971092

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00971092

Search

Navigation