(untitled) (Journal of Partial Differential Equations, 1993)
In this paper we are concemed with fully nonlinear elliptic equation F(x, u, Du, D²u) = 0. We establish the interior Lipschitz continuity and C^1,α regularity of viscosity solutions under natural structure conditions without differentiating the equation as usual, especially we give a new analytic Harnack inequality approach to C^1,α estimate for viscosity solutions instead of the geometric approach given by L. Caffarelli & L. Wang and improve their results. Our structure conditions are rather mild.