On homogenization for a periodic elliptic operator in a strip

St. Petersburg Mathematical Journal

Volumn 16, Issue 1, 2005, Pages 237-257

  Suslina, T A ^a  

^a ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

Author keywords

Effective operator; Homogenization; Periodic operator

Indexed keywords

EID: 85009799615     PISSN: 10610022     EISSN: 15477371     Source Type: Journal    
DOI: 10.1090/S1061-0022-04-00849-0     Document Type: Article

References (16)

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.MR0503330 (82h:35001)
2. N. S. Bakhvalov and G. P. Panasenko, Homogenization: averaging processes in periodic media. Mathematical problems in mechanics of composite materials, “Nauka,” Moscow, 1984
3. English transl., Math. Appl. (Soviet Ser.), vol. 36, Kluwer Acad. Publ. Group, Dordrecht, 1989.MR1112788 (92d:73002)
4. V. V. Zhikov, S. M. Kozlov, and O. A. Oleĭnik, Homogenization of differential operators, Fizmatgiz, Moscow, 1993
5. English transl., Springer-Verlag, Berlin, 1994.MR1329546 (96h:35003b)
6. V. V. Zhikov, Spectral approach to asymptotic diffusion problems, Differentsial’nye Uravneniya 25 (1989), no. 1, 44–50
7. English transl., Differential Equations 25 (1989), no. 1, 33–39.MR0986395 (90a:35107)
8. C. Conca and M. Vanninathan, Homogenization of periodic structures via Bloch decomposition, SIAM J. Appl. Math. 57 (1997), no. 6, 1639–1659.MR1484944 (98j:35017)
9. E. V. Sevost’yanova, Asymptotic expansion of the solution of a second-order elliptic equation with periodic rapidly oscillating coefficients, Mat. Sb. (N.S.) 115 (1981), no. 2, 204–222
10. English transl., Math. USSR-Sb. 43 (1982), no. 2, 181–198.MR0622145 (83d:35038)
11. 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.MR1882692 (2003f:35220)
12. M. Birman and T. Suslina, Second order periodic differential operators. Threshold properties and homogenization, Algebra i Analiz 15 (2003), no. 5, 1–108
13. English transl., St. Petersburg Math. J. 15 (2004), no. 5, 1–77.MR2068790
14. O. A. Ladyzhenskaya and N. N. Ural’tseva, Linear and quasilinear equations of elliptic type, 2nd ed., “Nauka”, Moscow, 1973
15. English transl. of 1st ed., Acad. Press, New York–London, 1968.MR0509265 (58:23009)
16. D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, Springer- Verlag, Berlin, 1998.MR0737190 (86c:35035)