Homogenization of a multidimensional periodic elliptic operator in a neighborhood of the edge of an internal gap

Journal of Mathematical Sciences

Volumn 136, Issue 2, 2006, Pages 3682-3690

  Birman, M Sh ^a   Suslina, T A ^a  

^a ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33744802664     PISSN: 10723374     EISSN: 15738795     Source Type: Journal    
DOI: 10.1007/s10958-006-0192-9     Document Type: Article

References (8)

1. M. Sh. Birman, "Discrete spectrum of the periodic Schrödinger operator perturbed by a decaying potential," Algebra Analiz, 8, 3-20 (1996).
2. M. Sh. Birman, "Discrete spectrum in gaps of a perturbed periodic Schrödinger operator. II. Nonregular perturbations," Algebra Analiz, 9, 62-89 (1997).
3. M. Sh. Birman, "Homogenization procedure for periodic operators near the edge of an internal gap," Algebra Analiz, 15, 61-71 (2003).
4. M. Sh. Birman and M. Z. Solomyak, "Estimates for singular numbers of integral operators," Usp. Mat. Nauk, 32, 17-84 (1977).
5. M. Sh. Birman and T. A. Suslina, "Threshold effects near the lower edge of the spectrum for periodic differential operators of mathematical physics," in: Systems, Approximations, Singular Integral Operators, and Related Topics (Bordeaux, 2000), Oper. Theory Adv. Appl, 129, Birkhäuser, Basel, (2001), pp. 71-107.
6. M. Sh. Birman and T. A. Suslina, "Second-order periodic differential operators. Threshold properties and homogenization," Algebra Analiz, 15, 1-108 (2003).
7. O. A. Ladyzhenskaya and N. N. Uraltseva, Linear and Quasilinear Elliptic Equations, Academic Press, New York-London (1968).
8. T. A. Suslina, "Discrete spectrum of a two-dimensional, periodic, elliptic, second-order operator perturbed by a decaying potential. II. Internal gaps," Algebra Analiz, 14, 128-189 (2002).