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(del u, D(2)u) = f(u) in the half plane, where f is locally Lipschitz continuous (with f(0) >= 0) and zero Dirichlet boundary conditions are imposed. The result is obtained without assuming the u or vertical bar del u vertical bar are bounded. (C) 2011 Elsevier Inc. All rights reserved.