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 |
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Pages (from-to) | 169-183 |
Number of pages | 15 |
Journal | Letters in Mathematical Physics |
Volume | 70 |
Issue number | 2 |
DOIs | |
Publication status | Published - 30 Nov 2004 |
Keywords
- bi-stable nematic devices
- liquid crystals
- harmonic maps
- polyhedra
- tangent boundary conditions
- lower bounds