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arXiv · 1303.0051

On the exponential decay of Laplacian eigenfunctions in planar domains with branches

Binh T. Nguyen·Andrey L. Delytsin·Denis S. Grebenkov
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Abstract

We consider the eigenvalue problem for the Laplace operator in a planar domain which can be decomposed into a bounded domain of arbitrary shape and elongated \branches" of variable cross-sectional profiles. When the eigenvalue is smaller than a prescribed threshold, the corresponding eigenfunction decays exponentially along each branch. We prove this behavior for Robin boundary condition and illustrate some related results by numerically computed eigenfunctions.

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Binh T. Nguyen, Andrey L. Delytsin, Denis S. Grebenkov. 2013-02-28. On the exponential decay of Laplacian eigenfunctions in planar domains with branches. https://arxiv.org/abs/1303.0051

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