Small volume expansion of the splitting of multiple Neumann Laplacian eigenvalues due to a grounded inclusion in two dimensions

Alexander Dabrowski

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arXiv · 1612.09095

Small volume expansion of the splitting of multiple Neumann Laplacian eigenvalues due to a grounded inclusion in two dimensions

Alexander Dabrowski

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Abstract

The first terms of the small volume asymptotic expansion for the splitting of Neumann boundary condition Laplacian eigenvalues due to a grounded inclusion of size ε are derived. An explicit formula to compute the first term from the eigenvalues and eigenfunctions of the unperturbed domain, the inclusion size and position is given. As a consequence, when an eigenvalue of double multiplicity splits in two distinct eigenvalues, one decays like O(1/log(ε)), the other like O(ε^2).

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Alexander Dabrowski. 2016-12-29. Small volume expansion of the splitting of multiple Neumann Laplacian eigenvalues due to a grounded inclusion in two dimensions. https://arxiv.org/abs/1612.09095

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