Geodesic
On a problem with nonperiodic frequent alternation of boundary conditions imposed on fast oscillating sets
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 2, pp. 284-294

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A singularly perturbed eigenvalue problem for the Laplacian in a cylinder is considered. The problem is characterized by frequent nonperiodic alternation of boundary conditions imposed on narrow strips lying on the cylinder's lateral surface. The width of the strips is an arbitrary function of a small parameter and can oscillate rapidly, with the nature of the oscillations being arbitrary. Sharp estimates are derived for the convergence rate of the eigenvalues and eigenfunctions in the problem. 
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     author = {D. I. Borisov},
     title = {On a~problem with nonperiodic frequent alternation of boundary conditions imposed on fast oscillating sets},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {284--294},
     publisher = {mathdoc},
     volume = {46},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_2_a8/}
}
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D. I. Borisov. On a problem with nonperiodic frequent alternation of boundary conditions imposed on fast oscillating sets. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 2, pp. 284-294. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_2_a8/