A note on comparison principles for viscosity solutions of fully nonlinear second order partial differential equations (Q1301355)

The goal of this paper is to compare viscosity sub- and supersolutions of fully nonlinear second order elliptic partial differential equations \(F(u,Du, D^2u)=0\) in \(\Omega\subset \mathbb{R}^N\), with Dirichlet boundary data \(u=f\) on \(\partial \Omega\), where \(F\in C(\mathbb{R}\times \mathbb{R}^N\times S(N))\) and \(f\in C(\partial \Omega)\). Two comparison principles are established.