Sur l'existence et la régularité de solutions radiales pour des équations de type Monge-Ampère complexe. (Existence and regularity of radial solutions for complex equations of Monge-Ampère type)
type: Item
instance of: scholarly article
title: Sur l'existence et la régularité de solutions radiales pour des équations de type Monge-Ampère complexe. (Existence and regularity of radial solutions for complex equations of Monge-Ampère type)
zbMATH Open document ID: 0655.35024
DOI: 10.1007/BF01474179
published in: Mathematische Annalen
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164349
review text: The author deals with existence and regularity of radial solutions to the homogeneous Dirichlet problem for the complex Monge-Ampère equation \(\det (\partial^ 2u/(\partial z_ j\partial \bar z_ j))=F(r,u,r(\partial u/\partial r))\) in the unit ball of \({\mathbb{C}}^ n,\) where \(r=| z|\) and \(F\geq 0\). If \(F(r,s,t)\leq C+\alpha \max (| s| \quad n,| t| \quad n)\) with \(\alpha <2^{-n}\) the existence of a \(C^{1,1/n}\)-solution is proved. Under an additional condition the solution is shown to be \(C^ 2\). If moreover \(F^{1/n}\in C^{\infty}\) then the solution is also smooth.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35J70
Mathematics Subject Classification ID: 35A30
zbMATH DE Number: 4069413
zbMATH Keywords: existence
zbMATH Keywords: regularity
zbMATH Keywords: radial solutions
zbMATH Keywords: homogeneous Dirichlet problem
zbMATH Keywords: complex Monge-Ampère equation
zbMATH Keywords: smooth
author: Makhlouf Derridj
reviewed by: F. Tomi
MaRDI profile type: Publication
cites work: The dirichlet problem for nonlinear second-order elliptic equations. II. Complex monge-ampère, and uniformaly elliptic, equations
cites work: Q3737761
cites work: Q4125259
cites work: Solving the degenerate complex Monge-Ampère equation with one concentrated singularity
cites work: Regularity of the complex Monge-Ampère equation for radially symmetric functions of the unit ball
description: scientific article; zbMATH DE number 4069413