Construction of singular solutions to the p-harmonic equation and its limit equation for \(p=\infty\)
type: Item
instance of: scholarly article
title: Construction of singular solutions to the p-harmonic equation and its limit equation for \(p=\infty\)
zbMATH Open document ID: 0594.35039
DOI: 10.1007/BF01172152
author: Gunnar Aronsson
published in: Manuscripta Mathematica
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155162
review text: Here, all solutions of the form \(u=r^ kf(\Phi)\) to the p-harmonic equation, \(div(| \nabla u|^{p-2}\nabla u)=0\) \((p>2)\) in the plane are determined. One main result is a representation formula for such solutions. Further, solutions with an isolated singularity at the origin are constructed (Theorem 1). Graphical illustrations are given at the end of the paper. Finally, all solutions \(u=r^ kf(\phi)\) of the limit equation for \(p=\infty\), \[ u^ 2_ xu_{xx}+2u_ xu_ yu_{xy}+u^ 2_ yu_{yy}=0, \] are constructed, some of which have a ''strong'' singularity at the origin (Theorem 2).
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35C99
zbMATH DE Number: 3955537
zbMATH Keywords: nonlinear elliptic equation
zbMATH Keywords: degenerate equation
zbMATH Keywords: quasi-radial
zbMATH Keywords: solution
zbMATH Keywords: p-harmonic equation
zbMATH Keywords: representation formula
zbMATH Keywords: isolated singularity
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3955537