Geodesic
On the spectrum of the Laplacian with frequently alternating boundary conditions
Teoretičeskaâ i matematičeskaâ fizika, Tome 118 (1999) no. 3, pp. 347-353 
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/
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     title = {On the spectrum of the {Laplacian} with frequently alternating boundary conditions},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[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