@article{ZVMMF_1996_36_7_a6,
author = {R. R. Gadyl'shin},
title = {On the perturbation of the {Laplacian} spectrum when the boundary condition type changes on a small part of the boundary},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {77--88},
year = {1996},
volume = {36},
number = {7},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_1996_36_7_a6/}
}
TY - JOUR AU - R. R. Gadyl'shin TI - On the perturbation of the Laplacian spectrum when the boundary condition type changes on a small part of the boundary JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 1996 SP - 77 EP - 88 VL - 36 IS - 7 UR - http://geodesic.mathdoc.fr/item/ZVMMF_1996_36_7_a6/ LA - ru ID - ZVMMF_1996_36_7_a6 ER -
%0 Journal Article %A R. R. Gadyl'shin %T On the perturbation of the Laplacian spectrum when the boundary condition type changes on a small part of the boundary %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 1996 %P 77-88 %V 36 %N 7 %U http://geodesic.mathdoc.fr/item/ZVMMF_1996_36_7_a6/ %G ru %F ZVMMF_1996_36_7_a6
R. R. Gadyl'shin. On the perturbation of the Laplacian spectrum when the boundary condition type changes on a small part of the boundary. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 36 (1996) no. 7, pp. 77-88. http://geodesic.mathdoc.fr/item/ZVMMF_1996_36_7_a6/
[1] Lord Rayleigh, “The theory of Helmholtz' resonator”, Proc. Roy. Soc. London. Ser. A, 92:638 (1916), 265–275 | DOI | Zbl
[2] Samarskii A. A., “O vliyanii zakrepleniya na sobstvennye chastoty zamknutykh ob'emov”, Dokl. AN SSSR, 63:6 (1948), 631–634 | MR
[3] Swanson C. A., “Asymptotic variational formulae for eigenvalues”, Canad. Math. Bull., 6:1 (1963), 1525 | MR
[4] Van Daik M., Metody vozmuschenii v mekhanike zhidkostei, Mir, M., 1967 | Zbl
[5] Sanches-Palensiya E., Neodnorodnye sredy i teoriya kolebanii, Mir, M., 1984 | MR
[6] Ilin A. M., Soglasovanie asimptoticheskikh razlozhenii reshenii kraevykh zadach, Nauka, M., 1989 | MR
[7] Oleinik O. A., Iosifyan G. A., Shamaev A. S., Matematicheskie zadachi teorii silno neodnorodnykh uprugikh sred, MGU, M., 1990
[8] Arsenev A. A., “Ob osobennostyakh analiticheskogo prodolzheniya i rezonansnykh svoistvakh resheniya zadachi rasseyaniya dlya uravneniya Gelmgoltsa”, Zh. vychisl. matem. i matem. fiz., 12:1 (1972), 112–138 | MR
[9] Fedoryuk M. V., “Zadacha Dirikhle dlya operatora Laplasa vo vneshnosti tonkogo tela vrascheniya”, Tr. seminara S. L. Soboleva, 1, Novosibirsk, 1980, 113–131 | MR | Zbl
[10] Ozawa S., “Singular variation of domains and eigenvalues of the Laplacian”, Duke Math. J., 48:4 (1981), 767–778 | DOI | MR | Zbl
[11] Mazya V. G., Nazarov S. A., Plamenevskii B. A., “Asimptoticheskie razlozheniya sobstvennykh chisel kraevykh zadach dlya operatora Laplasa v oblastyakh s malymi otverstiyami”, Izv. AN SSSR. Ser. matem., 48:2 (1984), 347–371 | MR
[12] Jimbo S., “The singularly perturbed domain and the characterization for the eigenfunctions with Neumann boundary condition”, J. Different. Equations, 77:2 (1989), 322–350 | DOI | MR | Zbl
[13] Hislop P. D., Martinez A., “Scattering resonances of Helmholtz resonator”, Indiana Univ. Math. J., 40:2 (1991), 767–788 | DOI | MR | Zbl
[14] Gadylshin P. P., “Metod sraschivaemykh asimptoticheskikh razlozhenii v zadache ob akusticheskom rezonatore Gelmgoltsa”, Prikl. matem. i mekhan., 56:3 (1992), 412–418 | MR
[15] Chechkin G. A., “Usrednenie kraevykh zadach s singulyarnym vozmuscheniem granichnykh uslovii”, Matem. sb., 184:6 (1993), 99–150 | MR | Zbl
[16] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973 | MR
[17] Gadylshin P. P., “Spektr ellipticheskikh kraevykh zadach pri singulyarnom vozmuschenii granichnykh uslovii”, Asimptotich. svoistva reshenii differents. ur-nii, BNTs UrO AN SSSR, Ufa, 1988, 3–15
[18] Gadylshin P. P., “Asimptotika sobstvennogo znacheniya singulyarno vozmuschennoi ellipticheskoi zadachi s malym parametrom v granichnom uslovii”, Differents. ur-niya, 22:4 (1986), 640–652 | MR
[19] Eskin G. I., Kraevye zadachi dlya ellipticheskikh psevdodifferentsialnykh uravnenii, Nauka, M., 1973 | MR
[20] Polia G., Sege G., Izoperimetricheskie neravenstva v matematicheskoi fizike, Fizmatgiz, M., 1962
[21] Landkof N. S., Osnovy sovremennoi teorii potentsiala, Nauka, M., 1966 | MR | Zbl
[22] Gadylshin P. P., “Rasscheplenie kratnogo sobstvennogo znacheniya zadachi Dirikhle dlya operatora Laplasa pri singulyarnom vozmuschenii granichnogo usloviya”, Matem. zametki, 52:4 (1992), 42–55 | MR
[23] Lavrentev M. A., Shabat B. V., Metody teorii funktsii kompleksnogo peremennogo, Nauka, M., 1973 | MR
[24] Gadylshin P. P., “Rasscheplenie kratnogo sobstvennogo znacheniya v kraevoi zadache dlya membrany, zakreplennoi na malom uchastke granitsy”, Sibirskii matem. zhurnal, 33:3 (1993), 43–61 | MR