Lower bound for energies of harmonic tangent unit-vector fields on convex polyhedra
نویسندگان
چکیده
We derive a lower bound for energies of harmonic maps of convex polyhedra in R 3 to the unit sphere S, 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. Mathematics Subject Classifications (2000). 58E20, 35J55.
منابع مشابه
S-valued harmonic maps on polyhedra with tangent boundary conditions
A unit-vector field n : P → S2 on a convex polyhedron P ⊂ R3 satisfies tangent boundary conditions if, on each face of P , n takes values tangent to that face. Tangent unit-vector fields are necessarily discontinuous at the vertices of P . We consider fields which are continuous elsewhere. We derive a lower bound E P (h) for the infimum Dirichlet energy Einf P (h) for such tangent unit-vector f...
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