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

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 (0
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11571/1441055
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