Comparison principle for singular degenerate elliptic equations on unbounded domains (Q807832)

The author announces a comparison principle for viscosity solutions of \(u+F(x,u,\nabla u,\nabla^ 2u)=0\) on an (unbounded) domain \(\Omega\) in \({\mathbb{R}}^ n\). The problem is supposed to be degenerate elliptic in the sense that \(F(x,r,p,X+Y)\leq F(x,r,p,X)\) for all \(x\in \Omega\), \(r\in {\mathbb{R}}\), \(p\in {\mathbb{R}}^ n\setminus \{0\}\) and X,Y symmetric linear operators on \({\mathbb{R}}^ n\) with \(Y\geq 0\).