On a free boundary problem for the \(p\)-Laplacian
type: Item
instance of: scholarly article
title: On a free boundary problem for the \(p\)-Laplacian
zbMATH Open document ID: 0893.35031
author: Elena Sartori
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-08-30T00:00:00Z
review text: The author considers the problem \[ \text{div} \bigl(| Du |^{p-2}Du \bigr) =0\quad\text{in}\quad\Omega_0- \Omega_1, \] \(u\to 1\), \(Du\to c_1\) uniformly a.e. as \(x\to \partial \Omega_1\), \(u\to 0\), \(Du\to c_0\) uniformly a.e. as \(x\to \partial\Omega_0\), where \(\Omega_1 \) and \(\Omega_0\) are bounded connected domains, \(\Omega_1 \subset \Omega_0\), that are starshaped with respect to the origin which is taken inside \(\Omega_1\). The author proves that the problem has a weak solution iff \(\Omega_0\) and \(\Omega_1\) are balls.
reviewed by: Marco Biroli
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 35B50
zbMATH DE Number: 1123514
zbMATH Keywords: \(p\)-Laplacian
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5755
OpenAlex ID: W1997370314
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DOI: 10.1006/JMAA.1997.5755
description: scientific article; zbMATH DE number 1123514