Estimates for solutions of quasilinear problems with dead cores
type: Item
instance of: scholarly article
title: Estimates for solutions of quasilinear problems with dead cores
zbMATH Open document ID: 1039.35031
author: Catherine Bandle
author: Stella Vernier Piro
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 2004-01-05T00:00:00Z
full work available at URL: 33 2003 Article 3203.pdf
review text: Let \(\Omega\subset\mathbb{R}^N\) be an arbitrary domain and \(a,b:\Omega\to \mathbb{R}^+\) be two functions. The authors consider boundary value problems of the form \[ \begin{cases} \sum^N_{i=1} (a(x)|\nabla u|^{p-2} u_{x_i})_{x_i}= b(x) f(u)\quad &\text{in }\Omega,\\ u= 1\quad &\text{on }\partial\Omega,\end{cases}\tag{1} \] where \(p\geq 1\) is a real number and \(f(s)\) is a nondecreasing function such that \(f(0)= 0\). The goal of the authors is to derive bounds for (1). To this end they use a Rayleigh-Faber-Krahn type inequality.
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 2021115
zbMATH Keywords: boundary value problems
zbMATH Keywords: Rayleigh-Faber-Krahn inequalities
zbMATH Keywords: a priori estimates
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
OpenAlex ID: W2056628268
DOI: 10.1007/S00033-003-3203-4
description: scientific article; zbMATH DE number 2021115