## Duke Mathematical Journal

### Subpotential lower bounds for nonnegative solutions to certain quasi-linear degenerate parabolic equations

#### Abstract

Nonnegative weak solutions of quasi-linear degenerate parabolic equations of $p$-Laplacian type are shown to be locally bounded below by Barenblatt-type subpotentials. As a consequence, nonnegative solutions expand their positivity set. That is, a quantitative lower bound on a ball $B_\rho$ at time $\bar{t}$ yields a quantitative lower bound on a ball $B_{2\rho}$ at some further time $t$. These lower bounds also permit one to recast the Harnack inequality of [4] in a family of alternative, equivalent forms

#### Article information

Source
Duke Math. J., Volume 143, Number 1 (2008), 1-15.

Dates
First available in Project Euclid: 23 May 2008

https://projecteuclid.org/euclid.dmj/1211574661

Digital Object Identifier
doi:10.1215/00127094-2008-013

Mathematical Reviews number (MathSciNet)
MR2414742

Zentralblatt MATH identifier
1170.35054

#### Citation

Dibenedetto, Emmanuele; Gianazza, Ugo; Vespri, Vincenzo. Subpotential lower bounds for nonnegative solutions to certain quasi-linear degenerate parabolic equations. Duke Math. J. 143 (2008), no. 1, 1--15. doi:10.1215/00127094-2008-013. https://projecteuclid.org/euclid.dmj/1211574661

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