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. 
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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/

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