The harnack inequality for second-order elliptic equations with divergence-free drifts

Mihaela Ignatova, Igor Kukavica, Lenya Ryzhik

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We consider an elliptic equation with a divergence-free drift b. We prove that an inequality of Harnack type holds under the assumption b∈Ln/2+δ where δ>0. As an application we provide a one-sided Liouville's theorem provided that b∈Ln/2+δ(ℝn).

Original languageEnglish (US)
Pages (from-to)681-694
Number of pages14
JournalCommunications in Mathematical Sciences
Volume12
Issue number4
DOIs
StatePublished - 2014

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Keywords

  • Drift-diffusion equations
  • Harnack inequality
  • Liouville theorem
  • Regularity

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