Extension and Representation of Divergence-free Vector Fields on Bounded Domains
Tosio Kato, Marius Mitrea, Gustavo Ponce, Michael Eugene Taylor · Mathematical Research Letters · 2000
Let Ω ⊂ Rn be a bounded, connected domain, with b + 1 boundary components, ∂Ω = Γ0∪ · · ·∪Γb. SayO0,...,Ob are the connected components of Rn\\Ω, O0 being the unbounded component, and Γj = ∂Oj. If b> 0, pick yj ∈ Oj, 1 ≤ j ≤ b, and set (1.1) gj(x):=