Geodesic
Convergence of eigenelements of a Steklov-type problem in a half-band with a small hole
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Spectral theory, Tome 141 (2017), pp. 42-47.

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We consider a Steklov-type problem for the Laplace operator in a half-band containing a small hole. On the lateral boundaries and the boundary of the hole, the Dirichlet conditions are stated, and on the base of the half-band the Steklov spectral condition. We prove that eigenvalues of this problem tend to zero as the small parameter (the “diameter” of the hole) vanishes.
Keywords: half-band, Steklov problem, eigenvalue, small hole
Mots-clés : singular perturbation, convergence. 
@article{INTO_2017_141_a2,
     author = {D. B. Davletov and O. B. Davletov},
     title = {Convergence of eigenelements of a {Steklov-type} problem in a half-band with a small hole},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {42--47},
     publisher = {mathdoc},
     volume = {141},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_141_a2/}
}
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D. B. Davletov; O. B. Davletov. Convergence of eigenelements of a Steklov-type problem in a half-band with a small hole. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Spectral theory, Tome 141 (2017), pp. 42-47. http://geodesic.mathdoc.fr/item/INTO_2017_141_a2/