We investigate two density questions for Sobolev, Besov and Triebel–Lizorkin spaces on rough sets. Our main results, stated in the simplest Sobolev space setting, are that: (i) for an open set Ω⊂Rn, D(Ω) is dense in {u∈Hs(Rn):suppu⊂Ω‾} whenever ∂Ω has zero Lebesgue measure and Ω is “thick” (in the sense of Triebel); and (ii) for a d-set Γ⊂Rn (0
Density results for Sobolev, Besov and Triebel–Lizorkin spaces on rough sets
Moiola A.
2021-01-01
Abstract
We investigate two density questions for Sobolev, Besov and Triebel–Lizorkin spaces on rough sets. Our main results, stated in the simplest Sobolev space setting, are that: (i) for an open set Ω⊂Rn, D(Ω) is dense in {u∈Hs(Rn):suppu⊂Ω‾} whenever ∂Ω has zero Lebesgue measure and Ω is “thick” (in the sense of Triebel); and (ii) for a d-set Γ⊂Rn (0File in questo prodotto:
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