On the spectrum of the Laplacian with frequently alternating boundary conditions
Teoretičeskaâ i matematičeskaâ fizika, Tome 118 (1999) no. 3, pp. 347-353
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We consider a boundary problem for the Laplacian in a two-dimensional domain with frequently alternating boundary conditions. The leading terms of the asymptotic expansions of the eigenvalues and the corresponding eigenfunctions are constructed under the assumption that the limiting case is the mixed boundary problem.
@article{TMF_1999_118_3_a3,
author = {D. I. Borisov and R. R. Gadyl'shin},
title = {On the spectrum of the {Laplacian} with frequently alternating boundary conditions},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {347--353},
year = {1999},
volume = {118},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1999_118_3_a3/}
}
TY - JOUR AU - D. I. Borisov AU - R. R. Gadyl'shin TI - On the spectrum of the Laplacian with frequently alternating boundary conditions JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1999 SP - 347 EP - 353 VL - 118 IS - 3 UR - http://geodesic.mathdoc.fr/item/TMF_1999_118_3_a3/ LA - ru ID - TMF_1999_118_3_a3 ER -
D. I. Borisov; R. R. Gadyl'shin. On the spectrum of the Laplacian with frequently alternating boundary conditions. Teoretičeskaâ i matematičeskaâ fizika, Tome 118 (1999) no. 3, pp. 347-353. http://geodesic.mathdoc.fr/item/TMF_1999_118_3_a3/
[1] G. A. Chechkin, Mat. sbornik, 184:6 (1993), 99–150 | MR | Zbl
[2] O. A. Oleinik, G. A. Chechkin, UMN, 48:6(294) (1993), 163–164 | MR | Zbl
[3] A. Friedman, C. Huang, J. Yong, Commun. Partial Differ. Equ., 20 (1/2) (1995), 59–102 | DOI | MR | Zbl
[4] N. N. Bogolyubov, Yu. A. Mitropolskii, Asimptoticheskie metody v teorii nelineinykh kolebanii, Nauka, M., 1974 | MR
[5] M. I. Vishik, L. A. Lyusternik, UMN, 12:5 (1957), 3–122 | MR | Zbl
[6] A. M. Ilin, Soglasovanie asimptoticheskikh razlozhenii reshenii kraevykh zadach, Nauka, M., 1989 | MR
[7] I. S. Gradshtein, I. M. Ryzhik, Tablitsy integralov, summ, ryadov i proizvedenii, Fizmatgiz, M., 1963 | MR