Perron’s Method and Barrier Functions for the Viscosity Solutions of the Dirichlet Problem for some Non-Linear Partial Differential Equations

Abstract

The Dirichlet problem for some non-linear partial differential equations via Perron’s method is studied in the viscosity set up, by considering two families of functions, instead of one, as considered by others before. The notion of barrier at a boundary point is introduced to study the regularity of boundary points. Barriers for some non-linear operators are also constructed.