An invariant Harnack inequality for a class of subelliptic operators under global doubling and Poincaré assumptions, and applications
type: Item
instance of: scholarly article
title: An invariant Harnack inequality for a class of subelliptic operators under global doubling and Poincaré assumptions, and applications
zbMATH Open document ID: 1382.35058
author: Erika Battaglia
author: Andrea Bonfiglioli
published in: Journal of Mathematical Analysis and Applications
publication date: 2018-01-11T00:00:00Z
review text: In this paper it is proved an invariant and non-homogeneous Harnack inequality for a class of subelliptic operators \(L\) in divergence form, with low-regular coefficients. It is assumed that \(L\) is associated to a Carnot-Carathédory doubling metric space, and it is assumed that a Poincaré inequality holds globally. It is proved that the Harnack inequality will hold true on every CC-ball. The authors give some applications to inner and boundary Hölder estimates, sharp results on the Green function for \(L\) and an explicit example of a class of operators that satisfy the assumptions of the paper. The Harnack inequality is also applied to the study of the existence of a fundamental solution \(\Gamma\) for \(L\).
reviewed by: Vincenzo Vespri
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35K10
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35H20
Mathematics Subject Classification ID: 35J08
zbMATH DE Number: 6824865
zbMATH Keywords: Carnot-Carathéodory spaces
zbMATH Keywords: doubling metric spaces
zbMATH Keywords: Poincaré inequality
zbMATH Keywords: operators in divergence form
zbMATH Keywords: low-regular coefficients
zbMATH Keywords: inner and boundary Hölder estimates
MaRDI profile type: Publication
full work available at URL: j.jmaa.2017.11.044
OpenAlex ID: W2772471789
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DOI: 10.1016/J.JMAA.2017.11.044
description: scientific article; zbMATH DE number 6824865