Alexandroff-Bakelman-Pucci estimate and Harnack inequality for degenerate/singular fully non-linear elliptic equations

This second version [of the WP version]includes additional results about quadratic non-linearities and a comparison with (and extension of) recent results.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.ou