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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Authors: Michel Chipot and Arnaud Rougirel
Journal: Trans. Amer. Math. Soc. 360 (2008), 3579-3602
MSC (2000): Primary 35P15, 35B40
Published electronically: January 9, 2008
MathSciNet review: 2386237
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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 Information

Michel Chipot
Affiliation: Institut für Mathematik, Universität Zürich, Winterthurerstr. 190, CH-8057 Zürich, Switzerland
Email: m.m.chipot@math.unizh.ch

Arnaud Rougirel
Affiliation: Laboratoire de Mathématiques et Applications, UMR 6086, Université de Poitiers & CNRS, Téléport 2 - BP 30179, Boulevard Marie et Pierre Curie, 86 962 Futuroscope Chasseneuil Cedex, France
Email: rougirel@math.univ-poitiers.fr

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04361-4
PII: S 0002-9947(08)04361-4
Keywords: Eigenvalue problems, $\ell$ goes to plus infinity
Received by editor(s): June 27, 2005
Received by editor(s) in revised form: April 24, 2006
Published electronically: January 9, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.