Let $u$ be a non-negative super-solution to a $1$-dimensional singular parabolic equation of $p$-Laplacian type ($1<p<2$). If $u$ is bounded below on a time-segment $\y\\times(0,T]$ by a positive number $M$, then it has a power-like decay of order $\frac p2-p$ with respect to the space variable $x$ in $\mathbb R\times[T/2,T]$. This fact, stated quantitatively in Proposition 1.1, is a "sidewise spreading of positivity" of solutions to such singular equations, and can be considered as a form of Harnack inequality. The proof of such an effect is based on geometrical ideas.

$1$-Dimensional Harnack Estimates

GIANAZZA, UGO PIETRO;
2016

Abstract

Let $u$ be a non-negative super-solution to a $1$-dimensional singular parabolic equation of $p$-Laplacian type ($1
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11571/1123782
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