A remark on the existence of viscosity solutions for quasilinear elliptic equations (Q2493836)

The paper deals with viscosity solutions to \(-\sum_{i,j=1}^n a_{ij}(x)u_{x_i x_j}+b(x,u,\nabla u)=0\) in a bounded, open domain \(\emptyset\neq\Omega\subset{\mathbb R}^n\) subject to a homogeneous Dirichlet boundary condition. The functions \(a, b\) are continuous, and the problem is supposed to be uniformly elliptic and proper in the sense of \textit{M. G. Crandall, H. Ishii} and \textit{P.-L. Lions} [Bull. Am. Math. Soc., New Ser. 27, No. 1, 1--67 (1992; Zbl 0755.35015)]. The author provides hypotheses under which Perron's method for viscosity solutions applies, and obtains existence and uniqueness results in this context.