Geodesic
The two terms asymptotics of the solutions of spectral problems with singular perturbations
Sbornik. Mathematics, Tome 69 (1991) no. 2, pp. 307-340

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Two groups of singularly perturbed boundary value problems for eigenvalues are considered. The first group contains the following types of perturbations: a small parameter in front of the leading derivatives in the equation or in the boundary condition, a domain with rapidly oscillating boundary, or a thin domain. Problems with perturbations of the data on a set with small diameter $\varepsilon$ constitute the second group. 
@article{SM_1991_69_2_a0,
     author = {S. A. Nazarov},
     title = {The two terms asymptotics of the solutions of spectral problems with singular perturbations},
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     number = {2},
     year = {1991},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1991_69_2_a0/}
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S. A. Nazarov. The two terms asymptotics of the solutions of spectral problems with singular perturbations. Sbornik. Mathematics, Tome 69 (1991) no. 2, pp. 307-340. http://geodesic.mathdoc.fr/item/SM_1991_69_2_a0/