We prove lower bounds for the Dirichlet energy of a unit vector field defined in a perforated domain of R 2 with nonzero degree on the outer boundary in terms of the total diameter of the holes. We use this to derive lower bounds, and then compactness results for sequences (u = ) of minimizers or al
β¦ LIBER β¦
Lower Bound for Energies of Harmonic Tangent Unit-Vector Fields on Convex Polyhedra
β Scribed by A. Majumdar; J. M. Robbins; M. Zyskin
- Publisher
- Springer
- Year
- 2004
- Tongue
- English
- Weight
- 183 KB
- Volume
- 70
- Category
- Article
- ISSN
- 0377-9017
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A mistake in the proof of Theorem 1 occurred which was pointed out to the author by Tristan RivieΓ re. It is stated there that the constant C depends only on the domain and the H 1Γ2 norm of the boundary data. It really should be the H s -norm for some s>1Γ2 for the result to be correct. The proble