Boundary asymptotics of the ergodic functions associated with fully nonlinear operators through a Liouville type theorem
type: Item
instance of: scholarly article
title: Boundary asymptotics of the ergodic functions associated with fully nonlinear operators through a Liouville type theorem
zbMATH Open document ID: 1479.35446
author: I. Birindelli
author: F. Demengel
author: Fabiana Leoni
published in: Discrete and Continuous Dynamical Systems
publication date: 2021-06-08T00:00:00Z
review text: The authors prove gradient boundary blow up rates for ergodic functions in bounded domains related to fully nonlinear degenerate/singular elliptic operators. Consider the following second order, fully nonlinear infinite boundary value problem \[ \left \{\begin{array}{ll} -F(D^2u)+|\nabla u|^\beta=0\ &\mbox{in}\ \mathbb{R}^N_+;\\ u(x',0)=+\infty \quad & \mbox{on} \ \partial \mathbb{R}^N_+, \end{array} \right.\tag{1} \] where \(\beta>1\), \(F:\mathcal{S}_N\to\mathbb{R}\) is a positively homogeneous uniformly elliptic operator, \(D^2u\) is the hessian matrix of the unknown function \(u\), and \(\nabla u\) is the gradient of \(u\). The first result is a Liouville-type classication theorem. Then the uniqueness, up to constants, of the ergodic functions, is obtained.
reviewed by: Shengbing Deng
Mathematics Subject Classification ID: 35J70
Mathematics Subject Classification ID: 35J75
Mathematics Subject Classification ID: 35B53
Mathematics Subject Classification ID: 35D40
zbMATH DE Number: 7356227
zbMATH Keywords: singular elliptic operators
zbMATH Keywords: degenerate elliptic operators
zbMATH Keywords: fully nonlinear operators
zbMATH Keywords: ergodic functions
zbMATH Keywords: Liouville-type theorems
MaRDI profile type: Publication
full work available at URL: dcds.2020395
OpenAlex ID: W3110949598
Wikidata QID: Q114022672
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DOI: 10.3934/DCDS.2020395
description: scientific article; zbMATH DE number 7356227