Ukrainian Mathematical Journal

, Volume 58, Issue 3, pp 398–417 | Cite as

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

  • V. A. Mikhailets
  • A. A. Murach


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.


Functional Parameter Pseudodifferential Operator Trace Operator Linear Differential Operator Topological Isomorphism 
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.


  1. 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).MathSciNetzbMATHGoogle Scholar
  2. 2.
    V. A. Mikhailets and A. A. Murach, “Improved scales of spaces and elliptic boundary-value problems. I,” Ukr. Mat. Zh., 58, No. 2, 217–235 (2006).CrossRefMathSciNetGoogle Scholar
  3. 3.
    L. Hörmander, Linear Partial Differential Operators, Springer, Berlin (1963).zbMATHGoogle Scholar
  4. 4.
    L. R. Volevich and B. P. Paneyakh, “Some spaces of generalized functions and imbedding theorems,” Usp. Mat. Nauk, 20, No. 1, 3–74 (1965).zbMATHGoogle Scholar
  5. 5.
    H. Triebel, Theory of Function Spaces [Russian translation], Mir, Moscow (1986).zbMATHGoogle Scholar
  6. 6.
    D. E. Edmunds and H. Triebel, Function Spaces, Entropy Numbers, Differential Operators, Cambridge Tracts Math., No. 120 (1999).Google Scholar
  7. 7.
    G. Shlenzak, “Elliptic problems in the improved scale of spaces,” Vestn. Mosk. Univ., No. 4, 48–58 (1974).Google Scholar
  8. 8.
    S. G. Krein (editor), Functional Analysis [in Russian], Nauka, Moscow (1972).Google Scholar
  9. 9.
    H. Triebel, Interpolation Theory, Function Spaces, Differential Operators [Russian translation], Mir, Moscow (1980).zbMATHGoogle Scholar
  10. 10.
    L. Hörmander, The Analysis of Linear Differential Operators. III. Pseudo-Differential Operators [Russian translation], Mir, Moscow (1987).Google Scholar
  11. 11.
    J.-L. Lions and E. Magenes, Problèmes aux Limites non Homogènes et Applications [Russian translation], Mir, Moscow (1971).zbMATHGoogle Scholar
  12. 12.
    M. S. Agranovich, “Elliptic boundary problems,” in: Encycl. Math. Sci., 79, Part. Different. Equat., Springer, Berlin (1997), pp. 1–144.Google Scholar
  13. 13.
    S. Agmon, A. Douglis, and L. Nirenberg, Estimates near the Boundary for Solutions of Elliptic Partial Difference Equations Satisfying General Boundary Conditions. I, Interscience, New York (1959).Google Scholar
  14. 14.
    Yu. V. Egorov, Linear Differential Equations of the Main Type [in Russian], Nauka, Moscow (1984).Google Scholar
  15. 15.
    Ya. A. Roitberg, Elliptic Boundary-Value Problems in the Spaces of Distributions, Kluwer, Dordrecht (1996).zbMATHGoogle Scholar
  16. 16.
    G. Geymonat, “Sui problemi ai limiti per i sistemi lineari ellittici,” Ann. Mat. Pura Appl., Ser. 4, 69, 207–284 (1965).zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • V. A. Mikhailets
    • 1
  • A. A. Murach
    • 2
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev
  2. 2.Chernigov Technological UniversityChernigov

Personalised recommendations