Nonlinear Liouville theorems for Grushin and Tricomi operators.
type: Item
instance of: scholarly article
title: Nonlinear Liouville theorems for Grushin and Tricomi operators.
zbMATH Open document ID: 1040.35012
DOI: 10.1016/S0022-0396(03)00138-4
author: Lorenzo D'Ambrosio
author: Sandra Lucente
published in: Journal of Differential Equations
publication date: 2003-11-10T00:00:00Z
review text: The paper concerns with necessary conditions for solvability of the inequality \[ L(x,y,D_x,D_y)u \geq | x|^{-\theta_1}| y|^{-\theta_2} | u|^q, \quad x\in \mathbb R^d,\;y\in \mathbb R^k, \tag{1} \] where \(L\) is a quasi-homogeneous operator, \[ L(f(\lambda^{\delta_1}.,\lambda ^{\delta_2}.))(x,y)=\lambda^h(Lf)(\lambda^{\delta_1}x, \lambda^{\delta_2}y). \] This class of operators includes degenerated elliptic equations in \(\mathbb R^N\). The authors prove that under suitable assumptions on \(\delta_i, \theta_i, h\) there exists a critical exponent \(q_c\) such that for \( 1< q\leq q_c\) there are no nontrivial solutions of (1).
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 35R45
Mathematics Subject Classification ID: 35J70
zbMATH DE Number: 2002193
zbMATH Keywords: degenerated elliptic equation
MaRDI profile type: Publication
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full work available at URL: s0022-0396(03)00138-4
OpenAlex ID: W1970009398
description: scientific article; zbMATH DE number 2002193