The asymptotics for the perfect conductivity problem with stiff \(C^{1,\alpha}\)-inclusions
type: Item
instance of: scholarly article
title: The asymptotics for the perfect conductivity problem with stiff \(C^{1,\alpha}\)-inclusions
zbMATH Open document ID: 1472.35103
author: Xia Hao
author: Zhiwen Zhao
published in: Journal of Mathematical Analysis and Applications
publication date: 2021-06-14T00:00:00Z
review text: Consider bounded domains \(D_1 \subset D \subset \mathbb R^n\) (\(n \geq 2\)) with the boundaries \(\partial D_1\) and \(\partial D\) being of \(C^{1,\alpha}\) (\(0 < \alpha < 1\)). Let \(\nu\) denote the outward unit normal to \(\partial D_1\). The authors discuss the boundary value problem \(\Delta u =0\) in \(D\backslash D_1\), \(u=C\) on \(\partial D_1\), \(\int_{\partial D_1} \frac{\partial u}{\partial \nu} ds =0\), \(u=\phi\) on \(\partial D\) with a given function \(\phi\) and an undetermined constant \(C\). Let \(\varepsilon\) denote the distance between \(\partial D_1\) and \(\partial D\). The authors investigate the behavior of \(u\) and \(\nabla u\) as \(\varepsilon \to 0\) when the curves become touching at one isolated point. The boundary and interior fields are estimated.
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35B44
zbMATH DE Number: 7358768
zbMATH Keywords: Laplace equation
zbMATH Keywords: boundary value problems
zbMATH Keywords: blow-up phenomena in highcontrast fiber-reinforced composites
reviewed by: Vladimir Mityushev
MaRDI profile type: Publication
full work available at URL: j.jmaa.2021.125201
OpenAlex ID: W3144646770
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DOI: 10.1016/J.JMAA.2021.125201
description: scientific article; zbMATH DE number 7358768