Asymptotics of simple eigenvalues and eigenfunctions for the Laplace operator in a domain with oscillating boundary
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 1, pp. 102-115
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The asymptotic behavior of solutions to spectral problems for the Laplace operator in a domain with a rapidly oscillating boundary is analyzed. The leading terms of the asymptotic expansions for eigenelements are constructed, and the asymptotics are substantiated for simple eigenvalues.
@article{ZVMMF_2006_46_1_a10,
author = {Y. Amirat and G. A. Chechkin and R. R. Gadyl'shin},
title = {Asymptotics of simple eigenvalues and eigenfunctions for the {Laplace} operator in a~domain with oscillating boundary},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {102--115},
publisher = {mathdoc},
volume = {46},
number = {1},
year = {2006},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_1_a10/}
}
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Y. Amirat; G. A. Chechkin; R. R. Gadyl'shin. Asymptotics of simple eigenvalues and eigenfunctions for the Laplace operator in a domain with oscillating boundary. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 1, pp. 102-115. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_1_a10/