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15 May 2008 Subpotential lower bounds for nonnegative solutions to certain quasi-linear degenerate parabolic equations
Emmanuele Dibenedetto, Ugo Gianazza, Vincenzo Vespri
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Duke Math. J. 143(1): 1-15 (15 May 2008). DOI: 10.1215/00127094-2008-013

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 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

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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

Information

Published: 15 May 2008
First available in Project Euclid: 23 May 2008

zbMATH: 1170.35054
MathSciNet: MR2414742
Digital Object Identifier: 10.1215/00127094-2008-013

Subjects:
Primary: 35B65, 35K65
Secondary: 35B45

Rights: Copyright © 2008 Duke University Press

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Vol.143 • No. 1 • 15 May 2008
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