Abstract
Nonnegative weak solutions of quasi-linear degenerate parabolic equations of -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 at time yields a quantitative lower bound on a ball at some further time . These lower bounds also permit one to recast the Harnack inequality of [4] in a family of alternative, equivalent forms
Citation
Emmanuele Dibenedetto. Ugo Gianazza. Vincenzo Vespri. "Subpotential lower bounds for nonnegative solutions to certain quasi-linear degenerate parabolic equations." Duke Math. J. 143 (1) 1 - 15, 15 May 2008. https://doi.org/10.1215/00127094-2008-013
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