Harnack inequalities for quasilinear anisotropic elliptic equations with a first order term

We consider weak solutions of the equation (Formula presented.) where H is in some cases called Finsler norm, Ω is a domain of RN, p>1, q≥max{p-1,1}, and a(·,u), f(·,u) are functions satisfying suitable assumptions. We exploit the Moser iteration technique to prove a Harnack type comparison inequality for solutions of the equation and a Harnack type inequality for solutions of the linearized operator. As a consequence, we deduce a Strong Comparison Principle for solutions of the equation and a Strong Maximum Principle for solutions of the linearized operator.