A counterexample concerning smooth approximation

Christopher J. Bishop

doi:10.1090/s0002-9939-96-03383-7

A counterexample concerning smooth approximation

Christopher J. Bishop

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We answer a question of Smith, Stanoyevitch and Stegenga in the negative by constructing a simply connected planar domain Ω with no two-sided boundary points and for which every point on Ω^c is an m₂-limit point of Ω^c and such that C^∞(Ω̄) is not dense in the Sobolev space W^k,p(Ω).

Original language	English
Pages (from-to)	3131-3134
Number of pages	4
Journal	Proceedings of the American Mathematical Society
Volume	124
Issue number	10
DOIs	https://doi.org/10.1090/s0002-9939-96-03383-7
State	Published - 1996

Keywords

Smooth approximation
Sobolev spaces

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10.1090/s0002-9939-96-03383-7

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title = "A counterexample concerning smooth approximation",

abstract = "We answer a question of Smith, Stanoyevitch and Stegenga in the negative by constructing a simply connected planar domain Ω with no two-sided boundary points and for which every point on Ωc is an m2-limit point of Ωc and such that C∞({\=Ω}) is not dense in the Sobolev space Wk,p(Ω).",

keywords = "Smooth approximation, Sobolev spaces",

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T1 - A counterexample concerning smooth approximation

AU - Bishop, Christopher J.

PY - 1996

Y1 - 1996

N2 - We answer a question of Smith, Stanoyevitch and Stegenga in the negative by constructing a simply connected planar domain Ω with no two-sided boundary points and for which every point on Ωc is an m2-limit point of Ωc and such that C∞(Ω̄) is not dense in the Sobolev space Wk,p(Ω).

AB - We answer a question of Smith, Stanoyevitch and Stegenga in the negative by constructing a simply connected planar domain Ω with no two-sided boundary points and for which every point on Ωc is an m2-limit point of Ωc and such that C∞(Ω̄) is not dense in the Sobolev space Wk,p(Ω).

KW - Smooth approximation

KW - Sobolev spaces

UR - https://www.scopus.com/pages/publications/33645920650

U2 - 10.1090/s0002-9939-96-03383-7

DO - 10.1090/s0002-9939-96-03383-7

M3 - Article

AN - SCOPUS:33645920650

SN - 0002-9939

VL - 124

SP - 3131

EP - 3134

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 10

ER -

A counterexample concerning smooth approximation

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