Geodesic
Two-Parameter Asymptotics in a Boundary-Value Problem for the Laplacian
Matematičeskie zametki, Tome 70 (2001) no. 4, pp. 520-534 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study a model boundary-value problem for the Laplacian in the unit disk with closely-spaced and periodic alternation of the type of boundary condition for the case in which the Dirichlet problem is the limit one. We study and justify the two-parameter asymptotics of an eigenvalue of the perturbed problem converging to a simple eigenvalue of the limit problem. 
@article{MZM_2001_70_4_a3,
     author = {D. I. Borisov},
     title = {Two-Parameter {Asymptotics} in a {Boundary-Value} {Problem} for the {Laplacian}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {520--534},
     year = {2001},
     volume = {70},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_70_4_a3/}
}
TY  - JOUR
AU  - D. I. Borisov
TI  - Two-Parameter Asymptotics in a Boundary-Value Problem for the Laplacian
JO  - Matematičeskie zametki
PY  - 2001
SP  - 520
EP  - 534
VL  - 70
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/MZM_2001_70_4_a3/
LA  - ru
ID  - MZM_2001_70_4_a3
ER  - 
%0 Journal Article
%A D. I. Borisov
%T Two-Parameter Asymptotics in a Boundary-Value Problem for the Laplacian
%J Matematičeskie zametki
%D 2001
%P 520-534
%V 70
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_2001_70_4_a3/
%G ru
%F MZM_2001_70_4_a3
D. I. Borisov. Two-Parameter Asymptotics in a Boundary-Value Problem for the Laplacian. Matematičeskie zametki, Tome 70 (2001) no. 4, pp. 520-534. http://geodesic.mathdoc.fr/item/MZM_2001_70_4_a3/

[1] Gadylshin R. R., “Ob asimptotike sobstvennykh znachenii dlya periodicheski zakreplennoi membrany”, Algebra i analiz, 10:1 (1998), 3–19 | MR | Zbl

[2] Friedman A., Huang C., Yong J., “Effective permeability of the boundary of the domain”, Comm. Partial Differential Equations, 20:1–2 (1995), 59–102 | DOI | MR | Zbl

[3] Chechkin G. A., “Usrednenie kraevykh zadach s singulyarnym vozmuscheniem granichnykh uslovii”, Matem. sb., 184:6 (1993), 99–150 | MR | Zbl

[4] Vatson G. N., Teoriya besselevykh funktsii, Ch. 1, IL, M., 1949

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