An Example on Sobolev Space Approximation
O'Farrell, Anthony G. (1997) An Example on Sobolev Space Approximation. Bulletin of the London Mathematical Society, 29 (4). pp. 470-474. ISSN 1469-2120
For each d ≥ 2 we construct a connected open set Ω ⊂ d 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).
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