A boundary Harnack inequality for singular equations of p-parabolic type

We prove a boundary Harnack type inequality for nonnegative solutions to singular equations of p-parabolic type, $2n/(n+1)<p<2$, in a time-independent cylinder whose base is $C^{1,1}$-regular. Simple examples show, using the corresponding estimates valid for the heat equation as a point of reference, that this type of inequality cannot, in general, be expected to hold in the degenerate case ($2<p<\infty$ )