The Blow-up Rate of Solutions to Boundary Blow-up Problems for the Complex Monge–Ampère Operator

A regularity result for solutions to boundary blow-up problems for the complex Monge–Ampère operator in balls in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{C}^n$$\end{document} is proved. For certain boundary blow-up problems on bounded, strongly pseudoconvex domains in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb C}^n$$\end{document} with smooth boundary an estimate of the blow-up rate of solutions are given in terms of the distance to the boundary and the product of the eigenvalues of the Levi form.