  In this paper, we study fully non-linear elliptic equations in non-divergence
form which can be degenerate when "the gradient is small". Typical examples are
either equations involving the $m$-Laplace operator or Bellman-Isaacs equations
from stochastic control problems. We establish an Alexandroff-Bakelman-Pucci
estimate and we prove a Harnack inequality for viscosity solutions of such
degenerate elliptic equations.
