Boundary Estimates for Certain Degenerate and Singular Parabolic Equations

We study the boundary behavior of non-negative solutions to a class of
degenerate/singular parabolic equations, whose prototype is the parabolic
$p$-Laplacian. Assuming that such solutions continuously vanish on some
distinguished part of the lateral part $S_T$ of a Lipschitz cylinder, we prove
Carleson-type estimates, and deduce some consequences under additional
assumptions on the equation or the domain. We then prove analogous estimates
for non-negative solutions to a class of degenerate/singular parabolic
equations, of porous medium type.