On the Phragmén–Lindelöf principle for second-order elliptic equations

Abstract

This paper is concerned with the maximum principle for subsolutions of second-order elliptic equations in non-divergence form in unbounded domains. Eventually the zero-order term can change sign and the involved functions can be unbounded at infinity with an admissible growth depending on the geometric properties of the domain. Following Gilbarg and Hopf, we also show a Phragmén–Lindelöf principle in angular sectors and give an example of an interesting field of application to nonlinear equations, deriving comparison principles for quasi-linear operators.