Chipot, M; Rougirel, A (2008). On the asymptotic behaviour of the eigenmodes for elliptic problems in domains becoming unbounded. Transactions of the American Mathematical Society, 360(7):3579-3602.
The aim of this work is to analyze the asymptotic behaviour of the eigenmodes of some elliptic eigenvalue problems set on domains becoming unbounded in one or several directions. In particular, in the case of a linear elliptic operator in divergence form, we prove that the sequence of the $ k$-th eigenvalues convergences to the first eigenvalue of an elliptic problems set on the section of the domain. Moreover, an optimal rate of convergence of this sequence is given.
The aim of this work is to analyze the asymptotic behaviour of the eigenmodes of some elliptic eigenvalue problems set on domains becoming unbounded in one or several directions. In particular, in the case of a linear elliptic operator in divergence form, we prove that the sequence of the $ k$-th eigenvalues convergences to the first eigenvalue of an elliptic problems set on the section of the domain. Moreover, an optimal rate of convergence of this sequence is given.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > General Mathematics
Physical Sciences > Applied Mathematics |
| Language: | English |
| Date: | 2008 |
| Deposited On: | 14 Jan 2009 06:40 |
| Last Modified: | 01 Dec 2023 02:47 |
| Publisher: | American Mathematical Society |
| ISSN: | 0002-9947 |
| Additional Information: | First published in Chipot, M; Rougirel, A (2008). On the asymptotic behaviour of the eigenmodes for elliptic problems in domains becoming unbounded. Transactions of the American Mathematical Society, 360(7):3579-3602, published by the American Mathematical Society. |
| OA Status: | Hybrid |
| Publisher DOI: | https://doi.org/10.1090/S0002-9947-08-04361-4 |
| Related URLs: | http://www.ams.org/mathscinet-getitem?mr=2386237 |
Chipot, M