  We prove local boundedness, Harnack's inequality and local regularity for
weak solutions of quasilinear degenerate elliptic equations in divergence form
with Rough coefficients. Degeneracy is encoded by a non-negative, symmetric,
measurable matrix valued function Q(x) and two suitable non-negative weight
functions. We setup an axiomatic approach in terms of suitable geometric
conditions and local Sobolev-Poincar\'e inequalities. Data integrability is
close to L1 and is exploited in terms of a suitable Stummel-Kato class that in
some cases is necessary for local regularity.
