Harnack inequality for a class of strongly degenerate elliptic operators formed by Hörmander vector fields
type: Item
instance of: scholarly article
title: Harnack inequality for a class of strongly degenerate elliptic operators formed by Hörmander vector fields
zbMATH Open document ID: 1225.35104
author: Juan-Miguel Gracia
published in: Manuscripta Mathematica
publication date: 2011-08-16T00:00:00Z
review text: This paper deals with the following strongly degenerate elliptic equation in divergence form \[ -X_j^*(a_{ij}X_iu+d_ju)+b_iX_iu+cu=f-X_i^*h_i. \] The authors prove the local boundedness of solutions and deduce a Harnack-type inequality. These properties enable them to show that the weak solutions to the above equation are continuous with respect to the Carnot-Carathéodory metric.
reviewed by: Vicenţiu D. Rădulescu
Mathematics Subject Classification ID: 35J70
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35D30
zbMATH DE Number: 5939576
zbMATH Keywords: strongly degenerate elliptic operator
zbMATH Keywords: Harnack inequality
zbMATH Keywords: Hörmander vector field
MaRDI profile type: Publication
full work available at URL: s00229-010-0420-y
OpenAlex ID: W2090908924
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DOI: 10.1007/S00229-010-0420-Y
description: scientific article; zbMATH DE number 5939576