Singular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin planar domains

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dc.creatorBorisov, Denis
dc.creatorFreitas, Pedro
dc.date2007-12-19
dc.date.accessioned2026-07-07T08:50:23Z
dc.date.available2026-07-07T08:50:23Z
dc.descriptionWe consider the Laplace operator with Dirichlet boundary conditions on a planar domain and study the effect that performing a scaling in one direction has on the spectrum. We derive the asymptotic expansion for the eigenvalues and corresponding eigenfunctions as a function of the scaling parameter around zero. This method allows us, for instance, to obtain an approximation for the first Dirichlet eigenvalue for a large class of planar domains, under very mild assumptions.
dc.identifierhttps://arxiv.org/abs/0712.3245
dc.identifierhttp://arxiv.org/abs/0712.3245
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/144591
dc.subjectSpectral Theory
dc.subjectMathematical Physics
dc.titleSingular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin planar domains
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