Harnack inequality for a class of degenerate elliptic operators.

The authors prove a Harnack inequality for a class two weights degenerate elliptic equations related with continuous Grushin-type vector fields. They define a distance related with the vector fields and they consider rectangle-type sets relative to this metric structure. Cut-off functions between this type of sets are exhibited and the result is proved by means of Moser iteration technique using a Sobolev-Poincaré inequality given by Franchi-Gutierrez and Wheeden.