In this paper, we study the regularity, the uniqueness and the asymptotic behavior of the solutions to a class of nonlinear operators in dependence of the summability properties of the datum $f$ and of the initial datum $u_0$. The case of only summable data $f$ and $u_0$ is allowed. We prove that these equations satisfy surprising regularization phenomena. Moreover, we prove estimates (depending continuously from the data) that for zero datum $f$ become well known decay (or ultracontractive) estimates.
"Regularity and time behavior of the solutions of linear and quasilinear parabolic equations." Adv. Differential Equations 23 (5/6) 329 - 372, May/June 2018.