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

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  • 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.

    Mathematics Subject Classification: Primary: 35J70, 35J75; Secondary: 35B53, 35D40.

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