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Journal Articles Journal of Spectral Theory Year : 2014

Dirichlet eigenvalues of cones in the small aperture limit

Abstract

We are interested in finite cones of fixed height 1 parametrized by their opening angle. We study the eigenpairs of the Dirichlet Laplacian in such domains when their apertures tend to 0. We provide multi-scale asymptotics for eigenpairs associated with the lowest eigenvalues of each fiber of the Dirichlet Laplacian. In order to do this, we investigate the family of their one-dimensional Born-Oppenheimer approximations. The eigenvalue asymptotics involves powers of the cube root of the aperture, while the eigenfunctions include simultaneously two scales.
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Dates and versions

hal-00802302 , version 1 (19-03-2013)
hal-00802302 , version 2 (24-10-2013)

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Thomas Ourmières-Bonafos. Dirichlet eigenvalues of cones in the small aperture limit. Journal of Spectral Theory, 2014, 4 (3), pp.485-513. ⟨10.4171/JST/77⟩. ⟨hal-00802302v2⟩
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