Rearrangements and the Monge-Ampère equations

We show that the direct counterpart of the Talenti symmetrization estimate for the Laplacian does not hold neither for the complex nor real Monge-Amp & egrave;re equations. We also use this Talenti result to improve some known estimates for subharmonic functions in C,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {C}},$$\end{document} where the constant depends on the area of the domain, instead of the diameter.