Recently I. Capuzzo Dolcetta, F. Leoni and A. Porretta obtain a very
surprising regularity result for fully nonlinear, superquadratic, elliptic
equations by showing that viscosity subsolutions of such equations are locally
H\"older continuous, and even globally if the boundary of the domain is regular
enough. The aim of this paper is to provide a simplified proof of their
results, together with an interpretation of the regularity phenomena, some
extensions and various applications