Boundary behavior in the Loewner-Nirenberg problem
type: Item
instance of: scholarly article
title: Boundary behavior in the Loewner-Nirenberg problem
zbMATH Open document ID: 1086.35019
author: Satyanad Kichenassamy
published in: Journal of Functional Analysis
publication date: 2005-06-01T00:00:00Z
review text: Let \(\Omega\subset \mathbb R^n\) be a bounded open domain of class \(C^{2+\alpha}\), \(0<\alpha<1\). The author considers the maximal solution \(u_\Omega\) of the problem (in \(\Omega\)) \[ \Delta u = n(n-2) u^{\frac{n+2}{n-2}} \] He proves that \(v_\Omega = u_\Omega^{-\frac{2}{n-2}}\) is of class \(C^{2+\alpha}\) up to the boundary. The proof uses the reduction of the problem to a nonlinear Fuchsian elliptic PDE.
reviewed by: Marco Biroli
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35C05
zbMATH DE Number: 2172987
zbMATH Keywords: Smoothness of solutions
zbMATH Keywords: Nonlinear elliptic problems
zbMATH Keywords: Solutions in closed forms
MaRDI profile type: Publication
full work available at URL: j.jfa.2004.06.014
OpenAlex ID: W2051620509
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DOI: 10.1016/J.JFA.2004.06.014
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description: scientific article; zbMATH DE number 2172987