  In this paper we study integro-differential equations like the anisotropic
fractional Laplacian. As in [Silvestre, Indiana University Mathematics Journal
55, 2006], we adapt the De Giorgi technique to achieve the
$C^{\gamma}$-regularity for solutions of class $C^{2}$ and use the geometry
found in [Caffarelli, Leit\~ao, and Urbano, Math. Ann. 360, 2014] to get an ABP
estimate, a Harnack inequality and the interior $C^{1, \gamma}$ regularity for
viscosity solutions.
