| Title:
|
Localization effects for eigenfunctions near to the edge of a thin domain (English) |
| Author:
|
Nazarov, Serguei A. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
127 |
| Issue:
|
2 |
| Year:
|
2002 |
| Pages:
|
283-292 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is proved that the first eigenfunction of the mixed boundary-value problem for the Laplacian in a thin domain $\Omega _h$ is localized either at the whole lateral surface $\Gamma _h$ of the domain, or at a point of $\Gamma _h$, while the eigenfunction decays exponentially inside $\Omega _h$. Other effects, attributed to the high-frequency range of the spectrum, are discussed for eigenfunctions of the mixed boundary-value and Neumann problems, too. (English) |
| Keyword:
|
spectral problem |
| Keyword:
|
thin domain |
| Keyword:
|
boundary layer |
| Keyword:
|
trapped mode |
| Keyword:
|
localized eigenfunction |
| MSC:
|
35B40 |
| MSC:
|
35J25 |
| MSC:
|
35P05 |
| MSC:
|
74B05 |
| MSC:
|
74E10 |
| MSC:
|
74G10 |
| idZBL:
|
Zbl 1022.74003 |
| idMR:
|
MR1981533 |
| DOI:
|
10.21136/MB.2002.134169 |
| . |
| Date available:
|
2012-10-05T13:02:25Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134169 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| . |
