Non-divergence parabolic equations of second order with critical drift in Lebesgue spaces

Gong Chen

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We consider uniformly parabolic equations and inequalities of second order in the non-divergence form with drift −ut+Lu=−ut+∑ijaijDiju+∑biDiu=0(≥0,≤0) in some domain Q⊂Rn+1. We prove growth theorems and the interior Harnack inequality as the main results. In this paper, we will only assume the drift b is in certain Lebesgue spaces which are critical under the parabolic scaling but not necessarily to be bounded. In the last section, some applications of the interior Harnack inequality are presented. In particular, we show there is a “universal” spectral gap for the associated elliptic operator. The counterpart for uniformly elliptic equations of second order in non-divergence form is shown in [19].

Original languageEnglish
Pages (from-to)2414-2448
Number of pages35
JournalJournal of Differential Equations
Issue number3
StatePublished - Feb 5 2017

Bibliographical note

Publisher Copyright:
© 2016 Elsevier Inc.


  • Harnack inequality
  • Measurable coefficients
  • Second-order parabolic equations
  • Spectral gap

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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