Liouville type theorem and decay estimates for solutions of fully nonlinear elliptic equation

Abstract

Liouville type theorems play crucial roles in proving the existence results of fully nonlinear elliptic equation and elliptic system. Boundedness assumptions of solutions are often imposed in deriving such Liouville type theorems. Although Liouville type theorems with boundedness assumption are enough in proving the existence result, it is interesting to study Liouville type theorem without boundedness assumption. This paper is devoted to establish some Liouville type theorems without boundedness assumption for fully nonlinear elliptic equation and elliptic system. At the same time, we prove some decay estimates for fully nonlinear elliptic equation and elliptic system.