Remote Access St. Petersburg Mathematical Journal

St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 
 

 

On homogenization procedure for periodic operators near the edge of an internal gap


Author: M. Sh. Birman
Translated by: T. A. Suslina
Original publication: Algebra i Analiz, tom 15 (2003), nomer 4.
Journal: St. Petersburg Math. J. 15 (2004), 507-513
MSC (2000): Primary 35P99
DOI: https://doi.org/10.1090/S1061-0022-04-00819-2
Published electronically: July 6, 2004
MathSciNet review: 2068979
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • 1. A. Bensoussan, J. L. Lions, and G. Papanicolaou, Asymptotic analysis for periodic structures, Stud. Math. Appl., vol. 5, North-Holland Publishing Co., Amsterdam-New York, 1978, 700 pp. MR 0503330 (82h:35001)
  • 2. N. S. Bakhvalov and G. P Panasenko, Homogenization of processes in periodic media, ``Nauka'', Moscow, 1984; English transl., Math. Appl. (Soviet. Ser.), vol. 36, Kluwer Acad. Publishers Group, Dordrecht, 1989. MR 0797571 (86m:73049)
  • 3. V. V. Zhikov, S. M. Kozlov, and O. A. Oleinik, Averaging of differential operators, ``Nauka'', Moscow, 1993; English transl., Homogenization of differential operators and integral functionals, Springer-Verlag, Berlin, 1994. MR 1318242 (96h:35003a)
  • 4. V. V. Zhikov, Spectral approach to asymptotic diffusion problems, Differentsial'nye Uravneniya 25 (1989), no. 1, 44-50; English transl., Differential Equations 25 (1989), no. 1, 33-39. MR 0986395 (90a:35107)
  • 5. C. Conca and M. Vanninathan, Homogenization of periodic structures via Bloch decomposition, SIAM J. Appl. Math. 57 (1997), no. 6, 1639-1659. MR 1484944 (98j:35017)
  • 6. M. Birman and T. Suslina, Threshold effects near the lower edge of the spectrum for periodic differential operators of mathematical physics, Systems, Approximation, Singular Integral Operators, and Related Topics (Bordeaux, 2000), Oper. Theory Adv. Appl., vol. 129, Birkhäuser, Basel, 2001, pp. 71-107. MR 1882692 (2003f:35220)
  • 7. M. Sh. Birman, Discrete spectrum in gaps of the perturbed periodic Schrödinger operator. . Nonregular perturbations, Algebra i Analiz 9 (1997), no. 6, 62-89; English transl., St. Petersburg Math. J. 9 (1998), no. 6, 1073-1095. MR 1610239 (99h:47054)
  • 8. M. Sh. Birman and M. Z. Solomyak, Estimates for the singular numbers of integral operators, Uspekhi Mat. Nauk 32 (1977), no. 1, 17-84; English transl., Russian Math. Surveys 32 (1977), no. 1, 15-89. MR 0438186 (55:11104)

Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2000): 35P99

Retrieve articles in all journals with MSC (2000): 35P99


Additional Information

M. Sh. Birman
Affiliation: Department of Physics, St. Petersburg State University, Ul’ynovskaya 1, Petrodvorets, St. Petersburg, 198504, Russia
Email: tanya@petrov.stoic.spb.su

DOI: https://doi.org/10.1090/S1061-0022-04-00819-2
Keywords: Periodic operators, homogenization, internal gaps, threshold effect
Received by editor(s): June 2, 2003
Published electronically: July 6, 2004
Additional Notes: Supported by RFBR (grant no. 02-01-00798).
Article copyright: © Copyright 2004 American Mathematical Society

American Mathematical Society