Perturbing fully nonlinear second order elliptic equations

Abstract

We present two types of perturbations with reverse effects on some scalar fully nonlinear second order elliptic differential operators: on the other hand, first order perturbations which destroy the global solvability of the Dirichlet problem, in smooth bounded domains of $\mathbb R^n$; on the other hand, an integral perturbation which restore the local solvability, on compact connected manifolds without boundary.