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 | |
| Publication status | Published - 30 Nov 2004 |
Keywords
- bi-stable nematic devices
- liquid crystals
- harmonic maps
- polyhedra
- tangent boundary conditions
- lower bounds
Cite this
Majumdar, A., Robbins, J. M., & Zyskin, M. (2004). Lower bounds for energies of harmonic tangent unit-vector fields on convex polyhedra. Letters in Mathematical Physics, 70(2), 169-183. https://doi.org/10.1007/s11005-004-4295-2