Geodesic
Asymptotic Expansion of Eigenvalues of the Laplace Operator in Domains with Singularly Perturbed Boundary
Matematičeskie zametki, Tome 78 (2005) no. 2, pp. 299-307.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we consider eigenvalue problems for the Laplace operator in three-dimensional domains with singularly perturbed boundary. Perturbations are generated by a complementary Dirichlet boundary condition on a small nonclosed surface inside the domain. The convergence and the asymptotic behavior of simple eigenvalues of the problem are considered. 
@article{MZM_2005_78_2_a15,
     author = {M. I. Cherdantsev},
     title = {Asymptotic {Expansion} of {Eigenvalues} of the {Laplace} {Operator} in {Domains} with {Singularly} {Perturbed} {Boundary}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {299--307},
     publisher = {mathdoc},
     volume = {78},
     number = {2},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_78_2_a15/}
}
TY  - JOUR
AU  - M. I. Cherdantsev
TI  - Asymptotic Expansion of Eigenvalues of the Laplace Operator in Domains with Singularly Perturbed Boundary
JO  - Matematičeskie zametki
PY  - 2005
SP  - 299
EP  - 307
VL  - 78
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2005_78_2_a15/
LA  - ru
ID  - MZM_2005_78_2_a15
ER  - 
%0 Journal Article
%A M. I. Cherdantsev
%T Asymptotic Expansion of Eigenvalues of the Laplace Operator in Domains with Singularly Perturbed Boundary
%J Matematičeskie zametki
%D 2005
%P 299-307
%V 78
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2005_78_2_a15/
%G ru
%F MZM_2005_78_2_a15
M. I. Cherdantsev. Asymptotic Expansion of Eigenvalues of the Laplace Operator in Domains with Singularly Perturbed Boundary. Matematičeskie zametki, Tome 78 (2005) no. 2, pp. 299-307. http://geodesic.mathdoc.fr/item/MZM_2005_78_2_a15/

[1] Landau L. D., Lifshits E. M., Kvantovaya mekhanika. Nerelyativistskaya teoriya, Nauka, M., 1974

[2] Ilin A. M., Soglasovanie asimptoticheskikh razlozhenii reshenii kraevykh zadach, Nauka, M., 1989 | MR

[3] Mazya V. G., Nazarov S. P., 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

[4] Gadylshin R. R., “Asimptotika sobstvennogo znacheniya singulyarno vozmuschennoi ellipticheskoi zadachi s malym parametrom v granichnom uslovii”, Differents. uravneniya, 22 (1986), 640–652 | MR

[5] Gadylshin R. R., “Rasscheplenie kratnogo sobstvennogo znacheniya zadachi Dirikhle dlya operatora Laplasa pri singulyarnom vozmuschenii granichnogo usloviya”, Matem. zametki, 52:4 (1992), 42–55

[6] Planida M. Yu., “O skhodimosti reshenii singulyarno vozmuschennykh kraevykh zadach dlya laplasiana”, Matem. zametki, 71:6 (2002), 867–877 | MR

[7] Planida M. Yu., “Ob asimptotike sobstvennykh znachenii dlya tsilindra, teploizolirovannogo na uzkoi polose”, ZhVMiMF, 43 (2003), 422–432

[8] Ladyzhenskaya O. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1973

[9] Mikhailov V. P., Differentsialnye uravneniya v chastnykh proizvodnykh, Nauka, M., 1976

[10] Sanches-Palensia E., Neodnorodnye sredy i teoriya kolebanii, Mir, M., 1984