Geodesic
Asymptotics of Eigenvalues of the Two-Dimensional Dirichlet Boundary-Value Problem for the Lam\'e Operator in a Domain with a Small Hole
Matematičeskie zametki, Tome 93 (2013) no. 4, pp. 537-548

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The Dirichlet boundary-value problem for the eigenvalues of the Lamé operator in a two-dimensional bounded domain with a small hole is studied. The asymptotics of the eigenvalue of this boundary-value problem is constructed and justified up to the power of the parameter defining the diameter of the hole.
Keywords: Dirichlet boundary-value problem, Lamé operator, Fredholm alternative, holomorphic function, asymptotics of eigenvalues, Bessel function. 
@article{MZM_2013_93_4_a4,
     author = {D. B. Davletov},
     title = {Asymptotics of {Eigenvalues} of the {Two-Dimensional} {Dirichlet} {Boundary-Value} {Problem} for the {Lam\'e} {Operator} in a {Domain} with a {Small} {Hole}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {537--548},
     publisher = {mathdoc},
     volume = {93},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_93_4_a4/}
}
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D. B. Davletov. Asymptotics of Eigenvalues of the Two-Dimensional Dirichlet Boundary-Value Problem for the Lam\'e Operator in a Domain with a Small Hole. Matematičeskie zametki, Tome 93 (2013) no. 4, pp. 537-548. http://geodesic.mathdoc.fr/item/MZM_2013_93_4_a4/