A short proof of the image-regularity of viscosity subsolutions for superquadratic viscous Hamilton–Jacobi equations and applications Original Research Article

Recently I. Capuzzo Dolcetta, F. Leoni and A. Porretta obtained a very surprising regularity result for fully nonlinear, superquadratic, elliptic equations by showing that viscosity subsolutions of such equations are locally Hölder 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.