  The main result of the paper is on the continuity of weak solutions of
infinitely degenerate quasilinear second order equations. Namely, we show that
every weak solution to a certain class of degenerate quasilinear equations is
continuous. More precisely, we show that it is H\"{o}lder continuous with
respect to a certain metric associated to the operator. One of the essential
features of this metric is that the metric balls are non doubling with respect
to Lebesgue measure. The proof of the continuity together with a recent result
by Rios et al. completes the result on hypoellipticity of a class of second
order quasilinear infinitely degenerate elliptic operators.
