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Quantitative analysis of eigenvalues and eigenfunctions for Robin Laplacian in bounded domains, suggesting new insights into boundary behaviors.
This paper deals with eigenelements of the Laplacian in bounded domains, under Robin boundary conditions, without any assumption on the sign of the Robin parameter. We quantify the asymptotics of the variation of simple eigenvalues under the singular perturbation produced by removing a shrinking set and imposing the same Robin condition on its boundary. We also study the convergence rate of the corresponding eigenfunctions.
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Felli et al. (2026) studied this question.
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