Geodesic
Characteristic frequencies of bodies with thin spikes. III. Frequency splitting
Matematičeskie zametki, Tome 61 (1997) no. 4, pp. 494-502 Cet article a éte moissonné depuis la source Math-Net.Ru

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The eigenvalue problem for the Laplace operator with the Neumann boundary conditions in a domain that has a thin spike of finite length is considered for the case in which the limit value is an eigenvalue both for the main body and the spike. The method of matched asymptotic expansions is used to construct total asymptotics of the eigenvalues of the perturbed problem and obtain closed formulas for the leading asymptotic terms. 
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     author = {R. R. Gadyl'shin},
     title = {Characteristic frequencies of bodies with thin {spikes.~III.} {Frequency} splitting},
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     year = {1997},
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R. R. Gadyl'shin. Characteristic frequencies of bodies with thin spikes. III. Frequency splitting. Matematičeskie zametki, Tome 61 (1997) no. 4, pp. 494-502. http://geodesic.mathdoc.fr/item/MZM_1997_61_4_a1/

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