@article{TIMM_2003_9_1_a6,
author = {R. R. Gadyl'shin},
title = {On domains with a~narrow isthmus in the critical case},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {50--55},
year = {2003},
volume = {9},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2003_9_1_a6/}
}
R. R. Gadyl'shin. On domains with a narrow isthmus in the critical case. Trudy Instituta matematiki i mehaniki, Asymptotic expansions, approximation theory, topology, Tome 9 (2003) no. 1, pp. 50-55. http://geodesic.mathdoc.fr/item/TIMM_2003_9_1_a6/
[1] Beale J. T., “Scattering frequencies of resonators”, Commun. Pure and Appl. Math., 26:4 (1973), 549–563 | DOI | MR | Zbl
[2] Arsenev A. A., “O suschestvovanii rezonansnykh polyusov i rezonansov pri rasseyanii v sluchae kraevykh uslovii II i III roda”, Zhurn. vychisl. matematiki i mat. fiziki, 16:3 (1976), 718–724 | MR
[3] Jimbo Sh., “The singularly perturbed domain and characterization for the eigenfunctions with Neumann boundary condition”, J. Differ. Equat., 77:2 (1989), 322–350 | DOI | MR | Zbl
[4] Hempel R., Seco L., Simon B., “The essential spectrum of Neumann Laplacians on some bounded singular domains”, J. Funct. Anal., 102 (1991), 448–483 | DOI | MR | Zbl
[5] Gadylshin P. P., “Asimptotika vtoroi sobstvennoi chastoty dlya sistemy dvukh tel, soedinennykh tonkoi peremychkoi”, Teoret. i mat. fizika, 97:1 (1993), 68–77 | MR
[6] Jimbo Sh., “Perturbation formula of eigenvalues in singularly perturbed domain”, J. Math. Soc. Japan, 45 (1993), 339–356 | DOI | MR | Zbl
[7] Gadylshin P. P., “O sobstvennykh chastotakh tel s tonkimi otrostkami. II. Asimptotiki”, Mat. zametki, 55:1 (1994), 20–34 | MR
[8] Brown R. M., Hislop P. D., Martinez A., “Eigenvalues and resonances for domains with tubes: Neumann boundary conditions”, J. Differ. Equat., 115 (1995), 458–476 | DOI | MR | Zbl
[9] Arrieta J. M., “Neumann eigenvalue problems on exterior perturbations of the domain”, J. Differ. Equat., 118 (1995), 54–103 | DOI | MR | Zbl
[10] Ilin A. M., Soglasovanie asimptoticheskikh razlozhenii reshenii kraevykh zadach, Nauka, M., 1989, 336 pp. | MR
[11] Gadylshin P. P., “Metod sraschivaniya asimptoticheskikh razlozhenii v zadache ob akusticheskom rezonatore Gelmgoltsa”, Prikl. matematika i mekhanika, 56:3 (1992), 412–418 | MR