Eigenvalues for the Robin Laplacian in domains with variable curvature
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- by Bernard Helffer and Ayman Kachmar PDF
- Trans. Amer. Math. Soc. 369 (2017), 3253-3287 Request permission
Abstract:
We determine accurate asymptotics for the low-lying eigenvalues of the Robin Laplacian when the Robin parameter goes to $-\infty$. The two first terms in the expansion have been obtained by K. Pankrashkin in the 2D-case and by K. Pankrashkin and N. Popoff in higher dimensions. The asymptotics display the influence of the curvature and the splitting between every two consecutive eigenvalues. The analysis is based on the approach developed by Fournais-Helffer for the semi-classical magnetic Laplacian. We also propose a WKB construction as candidate for the ground state energy.References
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Additional Information
- Bernard Helffer
- Affiliation: Université de Paris-Sud, Bât 425, 91405 Orsay, France – and – Laboratoire Jean Leray, Université de Nantes, 44300 Nantes, France
- MR Author ID: 83860
- Email: bernard.helffer@math.u-psud.fr
- Ayman Kachmar
- Affiliation: Department of Mathematics, Lebanese University, Hadath, Lebanon
- MR Author ID: 785084
- Email: ayman.kashmar@gmail.com
- Received by editor(s): January 13, 2015
- Received by editor(s) in revised form: April 29, 2015
- Published electronically: September 13, 2016
- © Copyright 2016 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 3253-3287
- MSC (2010): Primary 35P15, 47F05
- DOI: https://doi.org/10.1090/tran/6743
- MathSciNet review: 3605971