Lower bounds on the interaction between cavities connected by a thin tube
type: Item
instance of: scholarly article
title: Lower bounds on the interaction between cavities connected by a thin tube
zbMATH Open document ID: 0802.35109
DOI: 10.1215/S0012-7094-94-07306-7
author: R. M. Brown
author: André Martinez
author: Peter D. Hislop
published in: Duke Mathematical Journal
publication date: 1994-05-24T00:00:00Z
review text: The authors are concerned with a spectrum of the Dirichlet Laplacian in a Dumbbell shaped domain, which consists of 2 disjoint regions and a thin channel connecting them. It is interesting that the feature of extremal shape of the domain arises in the analytic quantity. The authors give a lower bound of the difference of the first 2 eigenvalues \(E_ 1\), \(E_ 2\) in terms of the size of the section of the thin channel. Such a study (splitting of eigenvalues) is an important subject in the spectral problem in many areas including the quantum mechanics (tunnel effect).
reviewed by: Shuichi Jimbo
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 572055
zbMATH Keywords: spectral gap
zbMATH Keywords: Dumbbell shaped domain
MaRDI profile type: Publication
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full work available at URL: s0012-7094-94-07306-7
OpenAlex ID: W1571049734
description: scientific article; zbMATH DE number 572055