Abstract approach to non homogeneous Harnack inequality in doubling quasi metric spaces. (April 2018)

• Record Type: Journal Article
• Authors: Guidi, Chiara; Montanari, Annamaria
• Is Part Of: Nonlinear analysis. Volume 169(2018)
• Page Start: 130
• Page End: 162
• Publication Date: 2018-04
• Subjects: 35J70 -- 35B45 -- 35B65; Invariant Harnack inequality -- Double ball property -- Critical density property -- Power decay property -- Doubling quasi-metric spaces -- Non divergence subelliptic PDEs with measurable coefficients -- Subelliptic equations -- Grushin vector fields -- Carnot–Carathéodory metric; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2017.12.009
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We develop an abstract theory to obtain Harnack inequality for non homogeneous PDEs in the setting of quasi metric spaces. The main idea is to adapt the notion of double ball and critical density property given by Di Fazio, Gutiérrez, Lanconelli, taking into account the right hand side of the equation. Then we apply the abstract procedure to the case of subelliptic equations in non divergence form involving Grushin vector fields and to the case of X-elliptic operators in divergence form.