Vol. 9, No. 5, 2016

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 10, 3371–3670
Issue 9, 2997–3369
Issue 8, 2619–2996
Issue 7, 2247–2618
Issue 6, 1871–2245
Issue 5, 1501–1870
Issue 4, 1127–1500
Issue 3, 757–1126
Issue 2, 379–756
Issue 1, 1–377

Volume 16, 10 issues

Volume 15, 8 issues

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1948-206X (online)
ISSN 2157-5045 (print)
 
Author index
To appear
 
Other MSP journals
On the negative spectrum of the Robin Laplacian in corner domains

Vincent Bruneau and Nicolas Popoff

Vol. 9 (2016), No. 5, 1259–1283
Abstract

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.

Keywords
Robin Laplacian, eigenvalues estimates, corner domains
Mathematical Subject Classification 2010
Primary: 35J10, 35P15, 47F05, 81Q10
Milestones
Received: 18 January 2016
Revised: 30 March 2016
Accepted: 29 April 2016
Published: 29 July 2016
Authors
Vincent Bruneau
Institut de Mathematiques
Université de Bordeaux I
351 Cours de La Libération
33405 Talence
France
Nicolas Popoff
Institut de Mathematiques
Université de Bordeaux I
351 Cours de La Libération
33405 Talence
France