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arXiv · 2011.06889

Gaps in the spectrum of two-dimensional square packing of stiff disks

L. D'Elia·S. A. Nazarov
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Abstract

In this paper we investigate via an asymptotic method the opening of gaps in the spectrum of a stiff problem for the Laplace operator $-\Delta$ in $\mathbb{R}^2$ perforated by contiguous circular holes. The density and the stiffness constants are of order $\varepsilon^{-2m}$ and $\varepsilon^{-1}$ in the holes with $m\in (0,1/2)$. We provide an explicit expression of the leading terms of the eigenvalues and the corresponding eigenfunctions which are related to the Bessel functions of the first kind.

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L. D'Elia, S. A. Nazarov. 2020-11-13. Gaps in the spectrum of two-dimensional square packing of stiff disks. https://arxiv.org/abs/2011.06889

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