Weak Harnack inequality for fully nonlinear uniformly elliptic pde with unbounded ingredients

The weak Harnack inequality for L^p-viscosity solutions is shown for fully nonlinear, second order uniformly elliptic partial differential equations with unbounded coefficients and inhomogeneous terms. This result extends those of Trudinger for strong solutions [21] and Fok for L ^p-viscosity solutions [13]. The proof is a modification of that of Caffarelli [5], [6], We apply the weak Harnack inequality to obtain the strong maximum principle, boundary weak Harnack inequality, global C^α estimates for solutions of fully nonlinear equations, strong solvability of extremal equations with unbounded coefficients, and Aleksandrov-Bakelman-Pucci maximum principle in unbounded domains.