Pointwise estimates for nonnegative solutions to a class of degenerate/singular parabolic equations

Let us consider a class of homogeneous quasilinear parabolic equations whose prototypes are the p-Laplacian and the Porous medium equation.
We assume suitable monotonicity and Lipschitz conditions that are suffcient to have a comparison principle, to preserve the positivity of solutions and to guarantee the existence of the solution of a Cauchy problem with L¹ initial
datum.
By using recent results obtained in collaboration with Bögelein, Calahorrano, Piro Vernier and Ragnedda we are able to give some pointwise estimates from above and from below starting from the value of the solution attained in a point. We apply these results to give sharp estimates to the fundamental solution of such class of equations.