Glaeser-type interpolation inequalities

I will present some recent results, in collaboration with A. Vitolo, concerning pointwise gradient estimates for nonnegative viscosity solutions of fully nonlinear second order elliptic equations. The results extend to a quite general nonlinear setting those of Yan Yan Li and Louis Nirenberg [Progress in Nonlinear Differential Equations and Their Applications, 66 (2005)] about the so-called Glaeser estimate for solutions of linear second-order elliptic equations.