$C^{1,\alpha}$ regularity of solutions of 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. H\"older estimates obtained by the first author (2011) are combined with new Lipschitz estimates obtained through the Ishii-Lions method in order to get $C^{1,\alpha}$ estimates for solutions of these equations. 
Cyril Imbert (LAMA), L. Silvestre
math.AP