On the exponential decay of Laplacian eigenfunctions in planar domains with branches
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.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2013
- DOI:
- 10.48550/arXiv.1303.0051
- arXiv:
- arXiv:1303.0051
- Bibcode:
- 2013arXiv1303.0051N
- Keywords:
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- Mathematical Physics
- E-Print:
- 9 pages, 7 figures