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

Binh T. Nguyen; Andrey L. Delytsin; Denis S. Grebenkov

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

Mathematical Physics 2016-10-05 v1 math.MP

Authors: Binh T. Nguyen , Andrey L. Delytsin , Denis S. Grebenkov

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.

Keywords

Laplacian eigenfunctions exponential decay planar domains Robin boundary condition eigenvalue problem

Cite

@article{arxiv.1303.0051,
  title  = {On the exponential decay of Laplacian eigenfunctions in planar domains with branches},
  author = {Binh T. Nguyen and Andrey L. Delytsin and Denis S. Grebenkov},
  journal= {arXiv preprint arXiv:1303.0051},
  year   = {2016}
}

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9 pages, 7 figures

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

Abstract

Keywords

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