The asymptotics of the solution to the Neumann spectral problem in a domain of the ``dense-comb'' type
type: Item
instance of: scholarly article
title: The asymptotics of the solution to the Neumann spectral problem in a domain of the ``dense-comb'' type
zbMATH Open document ID: 0930.35114
author: T. A. Mel'nik
author: Sergei A. Nazarov
published in: Journal of Mathematical Sciences (New York)
publication date: 1999-03-15T00:00:00Z
review text: The authors study a Neumann spectral problem for the Laplacian in a domain which consists of a fixed open set \(\Omega\) of \({\mathbb R}^2\) (the ``body'') to which are glued a large number \(N\) of thin rectangles (the ``teeth'') of length 1 and of width \(\varepsilon \sim N^{-1}\). Then they construct asymptotic solutions to this problem as \(\varepsilon\rightarrow 0\), using a particular matching method at the junction between \(\Omega\) and the teeth which lead to a spectral problem with discontinuous coefficients. Finally, they show that these constructions coincide to the actual solutions up to an error of order \({\mathcal O}(\varepsilon^{{1\over 2} -\delta})\) for any positive \(\delta\).
reviewed by: André Martinez
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35R05
zbMATH DE Number: 1259428
zbMATH Keywords: matching method
zbMATH Keywords: singular domain
zbMATH Keywords: asymptotic expansions
zbMATH Keywords: discontinuous coefficients
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1259428