Duke Mathematical Journal

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

Emmanuele Dibenedetto, Ugo Gianazza, and Vincenzo Vespri

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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 Bρ at time t̲ yields a quantitative lower bound on a ball B2ρ 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

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

First available in Project Euclid: 23 May 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K65: Degenerate parabolic equations 35B65: Smoothness and regularity of solutions
Secondary: 35B45: A priori estimates


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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