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 proved by the authors in the paper appeared in Acta Mathematica in a family of alternative, equivalent forms.
Sub--Potential Lower Bounds for Non--Negative Solutions to Certain Quasi--Linear Degenerate Parabolic Equations
GIANAZZA, UGO PIETRO;
2008-01-01
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 proved by the authors in the paper appeared in Acta Mathematica in a family of alternative, equivalent forms.File in questo prodotto:
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