Uniqueness and existence of maximal and minimal solutions of fully nonlinear elliptic PDE

Abstract

Two results are proved in the paper. The first is a uniqueness theorem for viscosity solutions of Dirichlet boundary value problems for Bellman-Isaacs equations with just measurable lower order terms. The second is a proof that there always exist maximal and minimal viscosity solutions of Dirichlet boundary value problems for fully nonlinear, uniformly elliptic PDE that are measurable in the $x$-variable.