Local behavior of singular positive solutions of semilinear elliptic equations with Sobolev exponent
type: Item
instance of: scholarly article
title: Local behavior of singular positive solutions of semilinear elliptic equations with Sobolev exponent
zbMATH Open document ID: 0839.35014
DOI: 10.1215/S0012-7094-95-07814-4
author: Chang-Shou Lin
author: Chiun-Chuan Chen
published in: Duke Mathematical Journal
publication date: 1996-06-19T00:00:00Z
review text: The authors study the semilinear equation \(-\Delta u= u^{(n+ 2)/(n- 2)}\) in \(\Omega\backslash Z\), where \(\Omega\) is an open domain in \(\mathbb{R}^n\) and \(Z\) a closed set. Their aim is to extend the results of Caffarelli, Gidas and Spruck who studied the equation on \(\mathbb{R}^n\backslash \{0\}\). Other nonlinearities \(f(u)\), that are close to this critical \(u^{(n+ 2)/(n- 2)}\), are also considered. The first result they prove is the following. If \(\text{Cap}(Z)= 0\) then positive solutions satisfy \(u(x)\leq Cd(x, Z)^{-(n- 2)/2}\) on \(B_R\) if \(B_{2R}\subset \Omega\). They claim that their approach will provide a simpler way to obtain the asymptotic result of Caffarelli, Gidas and Spruck. A consecutive paper in this direction is announced.
reviewed by: Guido Sweers
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 815764
zbMATH Keywords: singular solutions
zbMATH Keywords: critical Sobolev exponent
MaRDI profile type: Publication
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full work available at URL: s0012-7094-95-07814-4
OpenAlex ID: W1560973829
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description: scientific article; zbMATH DE number 815764