TY - JOUR
T1 - <em>C</em><sup>1,α</sup> Regularity of Viscosity Solutions of Fully Nonlinear Elliptic PDE Under Natural Structure Conditions
AU - Chen Yazhe
JO - Journal of Partial Differential Equations
VL - 3
SP - 193
EP - 216
PY - 1993
DA - 1993/06
SN - 6
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5710.html
KW - 
AB -  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 \&amp; L. Wang and improve their results. Our structure conditions are rather mild.