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

We consider weak solutions to $-Δ_pu+a(x,u)|\nabla u|^q=f(x,u),$ with $p>1$, $q\geq\max\,\{p-1,1\}$. 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.

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