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AN EXAMPLE ON SOBOLEV SPACE APPROXIMATION

Published online by Cambridge University Press:  01 July 1997

ANTHONY G. O'FARRELL
ANTHONY G. O'FARRELL
Affiliation:
St Patrick's College, Maynooth, Co. Kildare, Ireland
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Abstract

For each d[ges ]2 we construct a connected open set Ω⊂ℝd such that Ω=int (clos(Ω)), and for each k[ges ]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).

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 4 , July 1997 , pp. 470 - 474
Copyright
© The London Mathematical Society 1997

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