Skip to main content
SpringerLink
Log in

Improved scales of spaces and elliptic boundary-value problems. I

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We study improved scales of functional Hilbert spaces over ℝn and smooth manifolds with boundary. The isotropic Hörmander-Volevich-Paneyakh spaces are elements of these scales. The theory of elliptic boundary-value problems in these spaces is developed.

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

Similar content being viewed by others

References

  1. V. A. Mikhailets and A. A. Murach, “Elliptic operators in the improved scale of functional spaces, ” Ukr. Mat. Zh., 57, No. 5, 689–696 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  2. L. Hormander, Linear Partial Differential Operators, Springer, Berlin (1963).

    Google Scholar 

  3. L. R. Volevich and B. P. Paneyakh, “Some spaces of generalized functions and imbedding theorems, ” Usp. Mat. Nauk, 20, No. 1, 3–74 (1965).

    MATH  Google Scholar 

  4. H. Triebel, Theory of Function Spaces [Russian translation], Mir, Moscow (1986).

    MATH  Google Scholar 

  5. D. E. Edmunds and H. Triebel, Function Spaces, Entropy Numbers, Differential Operators, Cambridge Tracts Math., No. 120 (1999).

  6. G. Shlenzak, “Elliptic problems in the improved scale of spaces,” Vestn. Moscow Univ., No. 4, 48–58 (1974).

  7. L. de Haan, On Regular Variation and Its Application to the Weak Convergence of Sample Extremes, Math. Cent. Tracts., No. 32 (1970).

  8. E. Seneta, Regularly Varying Functions [Russian translation], Nauka, Moscow (1985).

    MATH  Google Scholar 

  9. N. H. Bingham, C. M. Goldie, and J. L. Teugels, Regular Variation, Cambridge Univ. Press, Cambridge (1989).

    MATH  Google Scholar 

  10. J. L. Geluk and L. de Haan, Regular Variation, Extensions and Tauberian Theorems, CWI Tract., No. 40 (1987).

  11. S. I. Reshnick, Extreme Values, Regular Variation, and Point Processes, Springer, New York (1987).

    Google Scholar 

  12. V. Maric, Regular Variation and Differential Equations, Springer, New York (2000).

    MATH  Google Scholar 

  13. S. G. Krein (editor), Functional Analysis [in Russian], Nauka, Moscow (1972).

    Google Scholar 

  14. J.-L. Lions and E. Magenes, Problèmes aux Limites non Homogènes et Applications [Russian translation], Mir, Moscow (1971).

    MATH  Google Scholar 

  15. N. Dunford and J. T. Schwartz, Linear Operators. Part I: General Theory [Russian translation], Inostr. Lit., Moscow (1962); Part II. Spectral Theory. Self-Adjoint Operators in Hilbert Space [Russian translation], Mir, Moscow (1966).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    V. A. Mikhailets

  2. Chernigov Technological University, Chernigov

    A. A. Murach

Authors
  1. V. A. Mikhailets
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. A. Murach
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 2, pp. 217–235, February, 2006.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mikhailets, V.A., Murach, A.A. Improved scales of spaces and elliptic boundary-value problems. I. Ukr Math J 58, 244–262 (2006). https://doi.org/10.1007/s11253-006-0064-y

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-006-0064-y

Keywords

Search

Navigation