Doubling properties for second order parabolic equations

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Abstract

We prove the doubling property of L-caloric measure corresponding to the second order parabolic equation in the whole space and in Lipschitz domains. For parabolic equations in the divergence form, a weaker form of the doubling property follows easily from a recent result, the backward Harnack inequality, and known estimates of Green's function. Our method works for both the divergence and nondivergence cases. Moreover, the backward Harnack inequality and estimates of Green's function are not needed in the course of proof.

Original languageEnglish (US)
Pages (from-to)313-327
Number of pages15
JournalAnnals of Mathematics
Volume150
Issue number1
DOIs
StatePublished - Jul 1999

Keywords

  • Doubling property
  • Fatou theorem
  • L-caloric measure

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