Anthony G. O’Farrell
Abstract
For each d⩾2 we construct a connected open set Ω ⊂ Rd such that Ω = int (clos(Ω)), and for each k ⩾ 1 and each p ∈ [1, ∞), the subset Wk, ∞(Ω) fails to be dense in the Sobolev space Wk, p(Ω), in the norm of Wk, p(Ω). 1991 Mathematics Subject Classification 46E35, 46F05.
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For each d⩾2 we construct a connected open set Ω ⊂ Rd such that Ω = int (clos(Ω)), and for each k ⩾ 1 and each p ∈ [1, ∞), the subset Wk, ∞(Ω) fails to be dense in the Sobolev space Wk, p(Ω), in the norm of Wk, p(Ω). 1991 Mathematics Subject Classification 46E35, 46F05.
Key concepts: Mathematics, Sobolev space, Mathematics Subject Classification, Norm (philosophy), Clos network, Space (punctuation), Open set, Pure mathematics