A localized boundary deformation which splits the spectrum of the Laplacian
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math.SP
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laplacianlocalizedspectrumsplitsarbitrarilyboundaryconstructdeformation
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For any Lipschitz domain we construct an arbitrarily small, localized perturbation which splits the spectrum of the Laplacian into simple eigenvalues. We use for this purpose a Hadamard's formula and spectral stability results.
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