On the comparison principle for second order elliptic equations without first and zeroth order terms

We consider the comparison principle for semicontinuous viscosity sub- and supersolutions of second order elliptic equations on the form F(Hw,x)=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F({\mathcal {H}}w,x) = 0$$\end{document}. A structural condition on the operator is presented that seems to unify the different existing theories. A new result is obtained and the proofs of the classical results are simplified.