\(L^ \infty\) boundedness of nonlinear eigenfunction under singular variation of domains
type: Item
instance of: scholarly article
title: \(L^ \infty\) boundedness of nonlinear eigenfunction under singular variation of domains
zbMATH Open document ID: 0855.35096
author: Shin Ozawa
published in: Osaka Journal of Mathematics
publication date: 1996-05-21T00:00:00Z
review text: The weak form of the nonlinear eigenvalue problem \[ - \Delta v_\varepsilon(x)= \lambda(\varepsilon) v_\varepsilon(x)^p,\quad p\in (0, 2), \] is studied in a domain \(M_\varepsilon= M- \overline B_\varepsilon\), where \(M\) has a smooth boundary and \(B_\varepsilon\) is a ball of radius \(\varepsilon\). The paper shows that the positive eigenfunctions are \(L^\infty\)-bounded by a constant which does not depend on \(\varepsilon\).
Mathematics Subject Classification ID: 35P30
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 880176
zbMATH Keywords: singular perturbation of the domain
reviewed by: Pavel Burda
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 880176