Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2006, Article ID 26845, 15 pages
http://dx.doi.org/10.1155/AAA/2006/26845

Lq-perturbations of leading coefficients of elliptic operators: Asymptotics of eigenvalues

Department of Mathematics, Linköping University, Linköping 58183, Sweden

Received 17 March 2006; Accepted 24 April 2006

Copyright © 2006 Vladimir Kozlov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. B. V. Boyarskiĭ, “Homeomorphic solutions of Beltrami systems,” Doklady Akademii Nauk SSSR, vol. 102, pp. 661–664, 1955 (Russian). View at Google Scholar · View at MathSciNet
  2. B. V. Boyarskiĭ, “On solutions of a linear elliptic system of differential equations in the plane,” Doklady Akademii Nauk SSSR, vol. 102, pp. 871–874, 1955 (Russian). View at Google Scholar · View at MathSciNet
  3. W. Cao and Y. Sagher, “Stability of Fredholm properties on interpolation scales,” Arkiv för Matematik, vol. 28, no. 2, pp. 249–258, 1990. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. T. Kato, “On the convergence of the perturbation method,” Journal of the Faculty of Science. University of Tokyo. Section I., vol. 6, pp. 145–226, 1951. View at Google Scholar · View at Zentralblatt MATH
  5. T. Kato, Perturbation Theory for Linear Operators, Springer, New York, 1984. View at Zentralblatt MATH
  6. N. Krugljak and M. Milman, “A distance between orbits that controls commutator estimates and invertibility of operators,” Advances in Mathematics, vol. 182, no. 1, pp. 78–123, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  7. V. Maz'ya, S. Nazarov, and B. Plamenevskij, Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains. Vol. I, vol. 111 of Operator Theory: Advances and Applications, Birkhäuser, Basel, 2000. View at MathSciNet
  8. V. Maz'ya, S. Nazarov, and B. Plamenevskij, Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains. Vol. II, vol. 112 of Operator Theory: Advances and Applications, Birkhäuser, Basel, 2000. View at MathSciNet
  9. N. G. Meyers, “An Lp-estimate for the gradient of solutions of second order elliptic divergence equations,” Annali della Scuola Normale Superiore di Pisa, Serie III, vol. 17, pp. 189–206, 1963. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. I. Ya. Shneiberg, “On the solvability of linear equations in interpolation families of Banach spaces,” Soviet Mathematics Doklady, vol. 14, pp. 1328–1331, 1973. View at Google Scholar · View at Zentralblatt MATH
  11. M. Zafran, “Spectral properties and interpolation of operators,” Journal of Functional Analysis, vol. 80, pp. 383–397, 1988. View at Publisher · View at Google Scholar