Lower bounds for energies of harmonic tangent unit-vector fields on convex polyhedra

Apala Majumdar, J. M. Robbins, M. Zyskin

Research output: Contribution to journalArticle

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Abstract

We derive a lower bound for energies of harmonic maps of convex polyhedra in R3 to the unit sphere S2 with tangent boundary conditions on the faces. We also establish that C∞ maps satisfying tangent boundary conditions are dense with respect to the Sobolev norm in the space of continuous tangent maps of finite energy.
Original languageUndefined/Unknown
Pages (from-to)169-183
Number of pages15
JournalLetters in Mathematical Physics
Volume70
Issue number2
DOIs
Publication statusPublished - 30 Nov 2004

Keywords

  • bi-stable nematic devices
  • liquid crystals
  • harmonic maps
  • polyhedra
  • tangent boundary conditions
  • lower bounds

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