Boundary asymptotics of the ergodic functions associated with fully nonlinear operators through a Liouville type theorem

Abstract

<p style='text-indent:20px;'>We prove gradient boundary blow up rates for ergodic functions in bounded domains related to fully nonlinear degenerate/singular elliptic operators. As a consequence, we deduce the uniqueness, up to constants, of the ergodic functions. The results are obtained by means of a Liouville type classification theorem in half-spaces for infinite boundary value problems related to fully nonlinear, uniformly elliptic operators.