Narrow domains and the harnack inequality for elliptic equations

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We present a direct proof of Moser's Harnack inequality that does not involve iterations. The method is based on a recursive estimate for solutions in domains of small measure. Such estimates can also be useful for other applications.

Original languageEnglish (US)
Pages (from-to)509-522
Number of pages14
JournalSt. Petersburg Mathematical Journal
Issue number3
StatePublished - 2016

Bibliographical note

Publisher Copyright:
© 2016 American Mathematical Society.


  • Harnack inequality
  • Measurable coefficients
  • Second-order elliptic equations


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