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)
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.
scientific article; zbMATH DE number 4069413