Classical solutions of singular Monge-Ampère equations in a ball
type: Item
instance of: scholarly article
title: Classical solutions of singular Monge-Ampère equations in a ball
zbMATH Open document ID: 1141.35373
author: Carlos A. Santos
author: José Valdo A. Gonçalves
published in: Journal of Mathematical Analysis and Applications
publication date: 2005-04-21T00:00:00Z
review text: The authors deal with the existence, uniqueness and regularity of convex, negative, radially symmetric classical solutions to the Dirichlet problem \[ \begin{gathered} \text{det}(D^2u)= \psi(x,-u)\quad\text{in }\mathbb{B},\\ u= 0\quad\text{on }\partial\mathbb{B},\end{gathered} \] where \((D^2 u)\) is the Hessian of \(u\), \(\mathbb{B}\subset\mathbb{R}^N\), \(N\geq 1\), is the unit ball with boundary \(\partial\mathbb{B}\), the function \(\psi: \mathbb{B}\times (0,\infty)\to [0,\infty)\) is continuous and radially symmetric in the first variable, that is, \(\psi(x,t):= \psi(|x|,t)\), where \(|x|\) is the Euclidean norm of \(x\). The main interest of the authors is when \(\psi\) is singular at \(|x|= 1\) and/or \(t= 0\). The authors employ fixed point arguments and the shooting method.
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 2159787
zbMATH Keywords: Singular Monge-Ampère equations
zbMATH Keywords: Radially symmetric solutions
zbMATH Keywords: Fixed points
zbMATH Keywords: Shooting method
zbMATH Keywords: Existence of solutions
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.11.019
OpenAlex ID: W1966242161
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DOI: 10.1016/J.JMAA.2004.11.019
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description: scientific article; zbMATH DE number 2159787