Analogs of Korn’s Inequality on Heisenberg Groups

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Abstract

We give two analogs of Korn’s inequality on Heisenberg groups. First, the norm of the horizontal differential is estimated in terms of the symmetric part of the differential. Second, Korn’s inequality is treated as a coercive estimate for a differential operator whose kernel coincides with the Lie algebra of the isometry group. For this purpose, we construct a differential operator whose kernel coincides with the Lie algebra of the isometry group on Heisenberg groups and prove a coercive estimate for the operator.

Original languageEnglish
Pages (from-to)846-860
Number of pages15
JournalSiberian Mathematical Journal
Volume60
Issue number5
DOIs
Publication statusPublished - 1 Sep 2019

Keywords

  • coercive estimate
  • Heisenberg group
  • integral representation formula
  • Korn inequality
  • Lie algebra of the isometry group

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