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On the asymptotic behaviour of the eigenmodes for elliptic problems in domains becoming unbounded


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.

Abstract

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.

Abstract

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2008
Deposited On:14 Jan 2009 06:40
Last Modified:05 Apr 2016 12:38
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.
Publisher DOI:https://doi.org/10.1090/S0002-9947-08-04361-4
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2386237

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