Keller–Osserman a priori estimates and the Harnack inequality for quasilinear elliptic and parabolic equations with absorption term

Abstract

In this article we study quasilinear equations model of which are Despite of the lack of comparison principle, we prove a priori estimates of Keller–Osserman type. Particularly under some natural assumptions on the function f, for nonnegative solutions of p-Laplace equation with absorption term we prove an estimate of the form with constant c independent of u, using this estimate we give a simple proof of the Harnack inequality. We prove a similar result for the evolution p-Laplace equation with absorption