Geodesic
Asymptotics of eigenvalues of the Dirichlet boundary value problem for the Lame operator in a three-dimensional domain with a small cavity
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 10, pp. 1847-1858

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A boundary value problem for the Lame operator in a bounded three-dimensional domain with a small cavity is studied. The domain is filled with an elastic homogeneous isotropic medium that is clamped at the boundary, which corresponds to the Dirichlet boundary condition. The leading term of an asymptotic expansion for the eigenvalue is constructed in the case of the Dirichlet limit problem. The asymptotic expansion is constructed in powers of a small parameter $\varepsilon$ that is the diameter of the cavity. 
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     author = {D. B. Davletov},
     title = {Asymptotics of eigenvalues of the {Dirichlet} boundary value problem for the {Lame} operator in a~three-dimensional domain with a~small cavity},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1847--1858},
     publisher = {mathdoc},
     volume = {48},
     number = {10},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_10_a6/}
}
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D. B. Davletov. Asymptotics of eigenvalues of the Dirichlet boundary value problem for the Lame operator in a three-dimensional domain with a small cavity. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 10, pp. 1847-1858. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_10_a6/