A Qualitative Phragmén–Lindelöf Theorem for Fully Nonlinear Elliptic Equations

We establish qualitative results of Phragmén–Lindelöf type for upper semicontinuous viscosity solutions of fully nonlinear partial differential inequalities of the second order in general unbounded domains of Rn, satisfying some measure-geometric property, but not necessarily regularity conditions. In particular, as for the Laplace equation, assuming elliptic structure conditions, the maximum principle holds in cylindrical and conical domains, provided that the solutions are supposed to have at most, respectively, an exponential or a polynomial growth.