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arXiv · 1911.09947

Concentration and confinement of eigenfunctions in a bounded open set (version 2)

Assia Benabdallah·Matania Ben-Artzi·Yves Dermenjian
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Abstract

Consider the Dirichlet-Laplacian in $\Omega:= (0,L)\times (0,H)$ and choose another open set $\omega\subset \Omega$. The estimate $0 C_{\omega}>0,\exists \omega, \omega\not=\emptyset$, such that $\inf R_{\omega}(u)=0$,and we wish to characterize these two sets. For two patterns we give a sufficient condition, sometimes necessary. As our operator corresponds to a layered media we can give another representation of its spectrum: i.e. a subset of points of $R\times R$ that leads to the suggested partition and others connected results: micro local interpretation, default measures,... Section 4.1 of the previous version was not correct, now it is corrected, many proofs are simplified and a new general result is added.

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Assia Benabdallah, Matania Ben-Artzi, Yves Dermenjian. 2019-11-22. Concentration and confinement of eigenfunctions in a bounded open set (version 2). https://arxiv.org/abs/1911.09947

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