Analogues of Korn’s Inequality on Heisenberg Groups

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Abstract

Abstract: Two analogues of Korn’s inequality on Heisenberg groups are constructed. First, the norm of the horizontal differential is estimated in terms of its symmetric part. 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 this operator. Additionally, a coercive estimate is proved for a differential operator whose kernel coincides with the Lie algebra of the group of conformal mappings on Heisenberg groups.

Original languageEnglish
Pages (from-to)181-184
Number of pages4
JournalDoklady Mathematics
Volume99
Issue number2
DOIs
Publication statusPublished - 1 Mar 2019

Keywords

  • DOMAINS
  • SPACES

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