Subpotential lower bounds for nonnegative solutions to certain quasi-linear degenerate parabolic equations
Subpotential lower bounds for nonnegative solutions to certain quasi-linear degenerate parabolic equations
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某些拟线性简并抛物线方程非负解的次势下界
DOI：
10.1215/00127094-2008-013
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发表时间：
2008
影响因子：
2.5
通讯作者：
V. Vespri
中科院分区：
文献类型：
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作者：
E. DiBenedetto;U. Gianazza;V. Vespri
证明了p - laplace型拟线性退化抛物型方程的非负弱解是由Barenblatt型子势局部有界的。因此，非负解扩展了它们的正集。也就是说，在时间t时球Bρ的定量下界会产生在更远的时间t时球B2ρ的定量下界。这些下界还允许人们将[1]的哈纳克不等式重新定义为一系列可选的等效形式。[10] E. DiBenedetto， U. Gianazza和V. Vespri，拟线性退化抛物型微分方程的harack估计，数学学报。(印刷中)。
Nonnegative weak solutions of quasilinear 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 t 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 [1] in a family of alternative, equivalent forms. References [1] E. DiBenedetto, U. Gianazza and V. Vespri, Harnack Estimates for Quasi–Linear Degenerate Parabolic Differential Equations, Acta Math. (in press).