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Journal articles

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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Contributor : Thomas Ourmières-Bonafos Connect in order to contact the contributor
Submitted on : Thursday, October 24, 2013 - 1:41:30 PM
Last modification on : Friday, May 20, 2022 - 9:04:47 AM
Long-term archiving on: : Monday, January 27, 2014 - 12:02:19 PM


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



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