Harnack estimates for non-negative weak solutions of a class of singular parabolic equations

We prove forward, backward and elliptic Harnack type inequalities for non-negative local weak solutions of singular parabolic differential equations of type u(t) = divA(x, t, u, Du) where A satisfies suitable structure conditions and a monotonicity assumption. The prototype is the parabolic p-Laplacian with 1 < p < 2. By using only the structure of the equation and the comparison principle, we generalize to a larger class of equations the estimates first proved by Bonforte et al. (Adv. Math. 224, 2151-2215, 2010) for the model equation.