A new proof of Hölder estimates for the gradient of quasilinear elliptic equations

In this paper, we give a new proof of Hölder estimates for the gradient of quasilinear elliptic equations, using a covering method inspired by the proof of Evans-Krylov theorem for fully nonlinear elliptic equations. Moreover, Hölder estimates for the gradient of fully nonlinear elliptic equations are also obtained by the same method.