C1,αC1,α regularity of solutions of some degenerate fully non-linear elliptic equations

In the present paper, a class of fully non-linear elliptic equations are considered, which are degenerate as the gradient becomes small. Hölder estimates obtained by the first author (2011) are combined with new Lipschitz estimates obtained through the Ishii–Lions method in order to get C1,αC1,α estimates for solutions of these equations.