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

Isabeau Birindelli; Françoise Demengel; Fabiana Leoni

doi:10.3934/dcds.2020395

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2021, Volume 41, Issue 7: 3021-3029. Doi: 10.3934/dcds.2020395

This issue Previous Article Next Article Global boundedness of solutions to the two-dimensional forager-exploiter model with logistic source

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

1.
Dipartimento di Matematica G. Castelnuovo, Sapienza Università di Roma, P.le A. Moro 2, 00185 Roma, Italy
2.
UMR 20-88, CY Paris University, 2, avenue Adolphe Chauvin, 95302 Cergy-Pontoise, France

^* Corresponding author
^* Corresponding author

Received: April 30, 2020

Revised: September 30, 2020

Early access: December 2020

Published: July 2021

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Abstract

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.

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

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