Mediterranean Journal of Mathematics

, Volume 1, Issue 1, pp 51–80

An Invariant Harnack Inequality for a Class of Hypoelliptic Ultraparabolic Equations

Original paper

DOI: 10.1007/s00009-004-0004-8

Cite this article as:
Kogoj, A. & Lanconelli, E. Mediterr. j. math. (2004) 1: 51. doi:10.1007/s00009-004-0004-8

Abstract

We show an invariant Harnack inequality for a class of hypoelliptic ultraparabolic operators with underlying homogeneous Lie group structures. As a byproduct we prove a Liouville type theorem for the related “stationary” operators. We also introduce a notion of link of homogeneous Lie Groups that allows us to show that our results apply to wide classes of operators.

Mathematics Subject Classification (2000).

Primary 35H10 31B05 Secondary 35A08 35B05 35K70 

Keywords.

Harnack inequalitye Hörmander operators Liouville theorems Homogeneous Lie groups 

Copyright information

© Birkhäuser-Verlag 2004

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di BolognaBolognaItaly
  2. 2.Dipartimento di MatematicaUniversità di BolognaBolognaItaly

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