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EnglishLet $u$ 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.
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| Titolo: | $1$-Dimensional Harnack Estimates |
| Autori: | |
| Data di pubblicazione: | 2016 |
| Rivista: | |
| Abstract: | 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. |
| Handle: | http://hdl.handle.net/11571/1123782 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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