  We prove Harnack inequality and local regularity results for weak solutions
of a quasilinear degenerate equation in divergence form under natural growth
conditions. The degeneracy is given by a suitable power of a strong $A_\infty$
weight. Regularity results are achieved under minimal assumptions on the
coefficients and, as an application, we prove $C^{1,\alpha}$ local estimates
for solutions of a degenerate equation in non divergence form.
