Double ball property for non-divergence horizontally elliptic operators on step two Carnot groups
type: Item
instance of: scholarly article
title: Double ball property for non-divergence horizontally elliptic operators on step two Carnot groups
zbMATH Open document ID: 1257.35190
DOI: 10.4171/RLM/632
author: Giulio Tralli
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 2013-01-21T00:00:00Z
review text: Summary: Let \(\mathcal L\) be a linear second order horizontally elliptic operator on a Carnot group of step two. We assume \(\mathcal L\) in non-divergence form and with measurable coefficients. Then, we prove the Double Ball Property for the nonnegative sub-solutions of \(\mathcal L\). With our result, in order to solve the Harnack inequality problem for this kind of operators, it becomes sufficient to prove the so called \(\epsilon\)-Critical Density.
Mathematics Subject Classification ID: 35R03
Mathematics Subject Classification ID: 35J70
zbMATH DE Number: 6127536
zbMATH Keywords: degenerate elliptic equation
zbMATH Keywords: invariant Harnack inequality
zbMATH Keywords: double ball property
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6127536