Partial regularity for weak solutions of nonlinear elliptic equations with supercritical exponents
type: Item
instance of: scholarly article
title: Partial regularity for weak solutions of nonlinear elliptic equations with supercritical exponents
zbMATH Open document ID: 1133.35357
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2005-02-23T00:00:00Z
review text: In the present paper, the author proves a partial regularity result for positive weak solutions of the equation \[ \Delta u+ h_1 u^\alpha+ h_2 u^\beta= 0\quad\text{in }\Omega, \] where \(\alpha\geq {n+2\over n-2}\), \(\alpha+ 1\geq 2\beta> 2\), \(h_i\in C^1(\Omega)\), \(i= 1,2\), \(a_i\leq h_i(x)\leq b_i\), \(0< a_i< b_i\) and \(|\nabla\log h_i(x)|\leq \beta\) for \(x\in\overline\Omega\), \(i= 1,2\). Here \(\Omega\) is an open subset of \(\mathbb R^n\) \((n\geq 3)\). To this end, the author uses the duality of a weighted Hardy space and a weighted BMO.
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35D30
Mathematics Subject Classification ID: 47J30
zbMATH DE Number: 2137246
zbMATH Keywords: partial regularity
zbMATH Keywords: Hausdorff dimension
zbMATH Keywords: weighted Hardy space
zbMATH Keywords: Morrey space
author: Song Bo Hou
MaRDI profile type: Publication
full work available at URL: j.na.2004.07.050
OpenAlex ID: W1990757093
cites work: Partial regularity for weak heat flows into spheres
cites work: Partial regularity for stationary harmonic maps into spheres
cites work: Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
cites work: The blow up locus of semilinear elliptic equations with supercritical exponents
cites work: Partial regularity for weak solutions of semilinear elliptic equations with supercritical exponents
cites work: Q4665462
cites work: Q4214811
cites work: The blow-up locus of heat flows for harmonic maps
cites work: Q5286841
cites work: Partial regularity for weak solutions of a nonlinear elliptic equation
cites work: Convergence and partial regularity for weak solutions of some nonlinear elliptic equation: The supercritical case
DOI: 10.1016/J.NA.2004.07.050
description: scientific article; zbMATH DE number 2137246