@Article{JPDE-6-193, author = {Chen Yazhe}, title = {C^1,α Regularity of Viscosity Solutions of Fully Nonlinear Elliptic PDE Under Natural Structure Conditions}, journal = {Journal of Partial Differential Equations}, year = {1993}, volume = {6}, number = {3}, pages = {193--216}, abstract = { 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.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5710.html} }