Asymptotic shape and location of small cores in elliptic free-boundary problems
type: Item
instance of: scholarly article
title: Asymptotic shape and location of small cores in elliptic free-boundary problems
zbMATH Open document ID: 0921.35024
DOI: 10.1007/PL00004636
published in: Mathematische Zeitschrift
publication date: 1999-03-07T00:00:00Z
review text: The paper deals with the boundary value problem \[ \mu^2\Delta u+g(u)=0 \quad \text{in }\Omega,\qquad u=0 \text{ on }\partial\Omega \] with \(g(\tau) =(\tau-1)^p_+\), \(\Omega\subset\mathbb{R}^n\), \(n\geq 3\). The authors investigate the asymptotic properties of the mountain pass solution as \(\mu\to 0\) and determine the asymptotic shape and location of the cores \(A_\mu\). It is proved that the cores \(A_\mu\) of the mountain pass solutions concentrate at a harmonic center of \(\Omega\) and that they are asymptotically spherical.
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 35J20
zbMATH DE Number: 1229589
zbMATH Keywords: location of cores
zbMATH Keywords: mountain pass solution
author: Martin Flucher
author: Juncheng Wei
reviewed by: Emil Minchev
MaRDI profile type: Publication
full work available at URL: pl00004636
OpenAlex ID: W2009518121
description: scientific article; zbMATH DE number 1229589