On the asymptotics of a Robin eigenvalue problem

Fioralba Cakoni 1 Nicolas Chaulet 2 Houssem Haddar 2
2 DeFI - Shape reconstruction and identification
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR7641
Abstract : The considered Robin problem can formally be seen as a small perturbation of a Dirichlet problem. However, due to the sign of the impedance value, its associated eigenvalues converge point-wise to −∞ as the perturbation goes to zero. We prove in this case that Dirichlet eigenpairs are the only accumulation points of the Robin eigenpairs with normalized eigenvectors. We then provide a criterion to select accumulating sequences of eigenvalues and eigenvectors and exhibit their full asymptotic with respect to the small parameter.
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Journal articles
Comptes Rendus Mathématique, Elsevier Masson, 2013, 351, pp.517-521. 〈10.1016/j.crma.2013.07.022〉
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Submitted on : Thursday, November 21, 2013 - 10:41:36 AM
Last modification on : Thursday, May 10, 2018 - 2:05:45 AM

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Fioralba Cakoni, Nicolas Chaulet, Houssem Haddar. On the asymptotics of a Robin eigenvalue problem. Comptes Rendus Mathématique, Elsevier Masson, 2013, 351, pp.517-521. 〈10.1016/j.crma.2013.07.022〉. 〈hal-00907355〉

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