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.

An Invariant Harnack Inequality for a Class of Hypoelliptic Ultraparabolic Equations

KOGOJ, ALESSIA ELISABETTA;
2004

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11576/2643002
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