On the asymptotics of a Robin eigenvalue problem

Fioralba Cakoni; Nicolas Chaulet; Houssem Haddar

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arXiv · 1307.8381

On the asymptotics of a Robin eigenvalue problem

Fioralba Cakoni·Nicolas Chaulet·Houssem Haddar

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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 $-\infty$ as the perturbation goes to zero. We prove that in this case, Dirichlet eigenpairs are the only accumulation points of the Robin eigenpairs with normalized eigenvectors. We then provide a criteria to select accumulating sequences of eigenvalues and eigenvectors and exhibit their full asymptotic with respect to the small parameter.

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Fioralba Cakoni, Nicolas Chaulet, Houssem Haddar. 2013-08-06. On the asymptotics of a Robin eigenvalue problem. https://arxiv.org/abs/1307.8381

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