The best Sobolev trace constant as limit of the usual Sobolev constant for small strips near the boundary
In this paper we prove that the best constant in the Sobolev trace embedding H1(Ω) → Lq(∂Ω) in a bounded smooth domain can be obtained as the limit as ε → 0 of the best constant of the usual Sobolev embedding H1(Ω) → Lq(ωε, dx/ε), where ω ε = {x ∈ Ω: dist (x, ∂Ω) < ε} is a small neighbourhood...
| Autores principales: | , , |
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| Formato: | JOUR |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_03082105_v138_n2_p223_Arrieta |
| Aporte de: |
| Sumario: | In this paper we prove that the best constant in the Sobolev trace embedding H1(Ω) → Lq(∂Ω) in a bounded smooth domain can be obtained as the limit as ε → 0 of the best constant of the usual Sobolev embedding H1(Ω) → Lq(ωε, dx/ε), where ω ε = {x ∈ Ω: dist (x, ∂Ω) < ε} is a small neighbourhood of the boundary. We also analyse symmetry properties of extremals of the latter embedding when Ω is a ball. © 2008 The Royal Society of Edinburgh. |
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