## T. Kuusi - G. Mingione - K. Nystrom

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

created by mingione on 06 Feb 2013

modified on 19 Sep 2014

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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 ($2 < p < ∞$)

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