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Zeitschrift für Analysis und ihre Anwendungen


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Volume 22, Issue 1, 2003, pp. 129–146
DOI: 10.4171/ZAA/1135

Published online: 2003-03-31

Harnack Inequality for a Class of Degenerate Elliptic Operators

Jose D. Fernandes[1], Jorge Groisman and Severino T. Melo[2]

(1) Universidade de São Paulo, Brazil
(2) Universidade de São Paulo, Brazil

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.

Keywords: Harnack-type inequality, degenerate elliptic equations

Fernandes Jose, Groisman Jorge, Melo Severino: Harnack Inequality for a Class of Degenerate Elliptic Operators. Z. Anal. Anwend. 22 (2003), 129-146. doi: 10.4171/ZAA/1135