The eigenvalues of the Laplacian on domains with small slits

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dc.creatorHillairet, Luc
dc.creatorJudge, Chris
dc.date2008-02-19
dc.date.accessioned2026-07-07T09:21:42Z
dc.date.available2026-07-07T09:21:42Z
dc.descriptionWe introduce a small slit into a planar domain and study the resulting effect upon the eigenvalues of the Laplacian. In particular, we show that as the length of the slit tends to zero, each real-analytic eigenvalue branch tends to an eigenvalue of the original domain. By combining this with our earlier work (arXiv:math/0703616), we obtain the following application: The generic multiply connected polygon has simple spectrum.
dc.description29 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/0802.2597
dc.identifierhttp://arxiv.org/abs/0802.2597
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/155118
dc.subjectSpectral Theory
dc.subjectAnalysis of PDEs
dc.subject35P99; 58J37
dc.titleThe eigenvalues of the Laplacian on domains with small slits
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