Singular variation of the ground state eigenvalue for a semilinear elliptic equation
type: Item
instance of: scholarly article
title: Singular variation of the ground state eigenvalue for a semilinear elliptic equation
zbMATH Open document ID: 0799.35087
author: Shin Ozawa
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1994-02-07T00:00:00Z
review text: The author studies the problem \(-\Delta u= \lambda u^ p\) in \(M_ \varepsilon\), \(u=0\) on \(\partial M_ \varepsilon\), \(u>0\) in \(M_ \varepsilon\). Here \(M_ \varepsilon\) is a bounded domain in \(\mathbb{R}^ 3\) with a ball of radius \(\varepsilon\) removed from the interior and \(1<p<5\). He considers the solution \(u_ \varepsilon\) which minimizes the natural constrained variational principle and the corresponding \(\lambda(\varepsilon)\). In particular, he studies how \(\lambda(\varepsilon)\) varies with \(\varepsilon\).
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35P30
zbMATH DE Number: 490580
zbMATH Keywords: domains with small holes
reviewed by: E. N. Dancer
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178225889
OpenAlex ID: W2024564716
cites work: Q4073917
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cites work: Q5187597
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DOI: 10.2748/TMJ/1178225889
description: scientific article; zbMATH DE number 490580