# A boundary Harnack inequality for singualr equations of $p$-parabolic type

created by mingione on 06 Feb 2013
modified on 19 Sep 2014

[BibTeX]

Published Paper

Inserted: 6 feb 2013
Last Updated: 19 sep 2014

Journal: Proc. Amer. Math. Soc.
Volume: 142
Pages: 2705-2719
Year: 2014

Abstract:

We prove a boundary Harnack type inequality for non-negative solutions to singular equations of $p$-parabolic type, $2n/(n + 1) < p < 2$, in 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 inequalities can not, in general, be expected to hold in the degenerate case ($2 < p < ∞$)