Monotonicity of solutions of Fully nonlinear uniformly elliptic equations in the half-plane

In this paper we study the monotonicity of positive (or non-negative) viscosity solutions to uniformly elliptic equations F(∇u,D2u)=f(u)F(∇u,D2u)=f(u) in the half plane, where f   is locally Lipschitz continuous (with f(0)⩾0f(0)⩾0) and zero Dirichlet boundary conditions are imposed. The result is obtained without assuming the u   or |∇u||∇u| are bounded.

► We consider viscosity solutions of Fully nonlinear equations. ► We provide maximum and comparison principles. ► We prove the monotonicity of positive solutions in the half-plane.