Harnack type inequalities for some doubly nonlinear singular parabolic equations

We prove Harnack type inequalities for a wide class of parabolic doubly nonlinear equations including uₜ= div(|u|ᵐ⁻¹|Du|ᵖ⁻²Du). We will distinguish between the supercritical range 3 - p/N subcritical2 < p+m ≤ 3 - p/N$ range. Our results extend similar estimates holding for general equations having the same structure as the parabolic $p$-Laplace or the porous medium equation and recently collected in [6].