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

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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).

Item Type: Article
Keywords: Sobolev Space approximation.
Academic Unit: Faculty of Science and Engineering > Mathematics and Statistics
Item ID: 1809
Identification Number: 10.1112/S0024609396002901
Depositing User: Prof. Anthony O'Farrell
Date Deposited: 25 Jan 2010 15:07
Journal or Publication Title: Bulletin of the London Mathematical Society
Publisher: Oxford University Press,
Refereed: No

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