Quasilinear elliptic equations with boundary blow-up
type: Item
instance of: scholarly article
title: Quasilinear elliptic equations with boundary blow-up
zbMATH Open document ID: 0893.35032
DOI: 10.1007/BF02787108
author: Jerk Matero
published in: Journal d'Analyse Mathématique
publication date: 1998-06-11T00:00:00Z
review text: This paper is devoted to the problem \(\triangle_pu(x)=f(u(x))\) in a bounded domain \(D\), \(u(x)\to\infty\) as \(x\to\partial D\), where \(\triangle_p\) is the \(p\)-Laplacian. The existence of a solution is proved and its asymptotic behaviour near the boundary is studied. As for the Laplacian it depends only on the nonlinearity and not on the geometry. The method relies on comparison functions and uses the maximum principle for \(p\)-Laplacians. The author also extends a method developed for the Laplacian by Bandle and Essen, for estimating the gradients to the more general operator. This method uses a scaling argument and applies to power nonlinearities.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35J67
zbMATH DE Number: 971865
zbMATH Keywords: \(p\)-Laplacian
zbMATH Keywords: asymptotic behaviour near the boundary
zbMATH Keywords: comparison functions
zbMATH Keywords: scaling argument
reviewed by: Catherine Bandle
MaRDI profile type: Publication
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description: scientific article