The classical Poincar\'e inequality establishes that for any bounded regular
domain Ω⊂RN there exists a constant C=C(Ω)>0 such that
∫Ω∣u∣2dx≤C∫Ω∣∇u∣2dx∀u∈H1(Ω),∫Ωu(x)dx=0. In this note we show that C
can be taken independently of Ω when Ω is in a certain class of
domains. Our result generalizes previous results in this direction.Comment: 12 pages, 1 figur