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

Apala Majumdar; J. M. Robbins; M. Zyskin

doi:10.1007/s11005-004-4295-2

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

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

Mathematics And Statistics

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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 language	Undefined/Unknown
Pages (from-to)	169-183
Number of pages	15
Journal	Letters in Mathematical Physics
Volume	70
Issue number	2
DOIs	https://doi.org/10.1007/s11005-004-4295-2
Publication status	Published - 30 Nov 2004

Keywords

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

Access to Document

10.1007/s11005-004-4295-2

Cite this

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title = "Lower bounds for energies of harmonic tangent unit-vector fields on convex polyhedra",

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.",

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AU - Robbins, J. M.

AU - Zyskin, M.

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N2 - 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.

AB - 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.

KW - bi-stable nematic devices

KW - liquid crystals

KW - harmonic maps

KW - polyhedra

KW - tangent boundary conditions

KW - lower bounds

U2 - 10.1007/s11005-004-4295-2

DO - 10.1007/s11005-004-4295-2

M3 - Article

VL - 70

SP - 169

EP - 183

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

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