On the Harnack inequality for quasilinear elliptic equations with a first order term

Abstract

We consider weak solutions to $$-{\Delta }_{p}u+a(x,u)|\nabla u{|}^q=f(x,u),$$ with $p>1$, $q\ge \max \{p-1,1\}$. We exploit the Moser iteration technique to prove a Harnack comparison inequality for $C^1$ weak solutions. As a consequence we deduce a strong comparison principle.