We prove a Harnack inequality for a class of two-weight degenerate elliptic operators. The metric distance is induced by continuous Grushin-type vector fields. It is not know whether there exist cutoffs fitting the metric balls. This obstacle is bypassed by means of a covering argument that allows the use of rectangles in the Moser iteration.
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Jose D. Fernandes, Severino T. Melo, Jorge Groisman, Harnack Inequality for a Class of Degenerate Elliptic Operators. Z. Anal. Anwend. 22 (2003), no. 1, pp. 129–146DOI 10.4171/ZAA/1135