Geodesic
Two-Parameter Asymptotics in a Boundary-Value Problem for the Laplacian
Matematičeskie zametki, Tome 70 (2001) no. 4, pp. 520-534

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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},
     publisher = {mathdoc},
     volume = {70},
     number = {4},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_70_4_a3/}
}
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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/