An invariant Harnack inequality for a class of subelliptic operators under global doubling and Poincaré assumptions, and applications (Q1688838)

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 \(L\).