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

Kuusi, Tuomo; Mingione, Giuseppe; Nyström, Kaj

doi:10.1090/S0002-9939-2014-12171-X

A boundary Harnack inequality for singular equations of $p$-parabolic type
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by Tuomo Kuusi, Giuseppe Mingione and Kaj Nyström

Proc. Amer. Math. Soc. 142 (2014), 2705-2719

DOI: https://doi.org/10.1090/S0002-9939-2014-12171-X

Published electronically: April 29, 2014

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Abstract:

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 ($2<p<\infty$).

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