Open Access
Translator Disclaimer
2016 On the negative spectrum of the Robin Laplacian in corner domains
Vincent Bruneau, Nicolas Popoff
Anal. PDE 9(5): 1259-1283 (2016). DOI: 10.2140/apde.2016.9.1259


For a bounded corner domain Ω, we consider the attractive Robin Laplacian in Ω with large Robin parameter. Exploiting multiscale analysis and a recursive procedure, we have a precise description of the mechanism giving the bottom of the spectrum. It allows also the study of the bottom of the essential spectrum on the associated tangent structures given by cones. Then we obtain the asymptotic behavior of the principal eigenvalue for this singular limit in any dimension, with remainder estimates. The same method works for the Schrödinger operator in n with a strong attractive δ-interaction supported on Ω. Applications to some Ehrling-type estimates and the analysis of the critical temperature of some superconductors are also provided.


Download Citation

Vincent Bruneau. Nicolas Popoff. "On the negative spectrum of the Robin Laplacian in corner domains." Anal. PDE 9 (5) 1259 - 1283, 2016.


Received: 18 January 2016; Revised: 30 March 2016; Accepted: 29 April 2016; Published: 2016
First available in Project Euclid: 12 December 2017

zbMATH: 06608425
MathSciNet: MR3531372
Digital Object Identifier: 10.2140/apde.2016.9.1259

Primary: 35J10 , 35P15 , 47F05 , 81Q10

Keywords: corner domains , eigenvalues estimates , Robin Laplacian

Rights: Copyright © 2016 Mathematical Sciences Publishers


Vol.9 • No. 5 • 2016
Back to Top