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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A counterexample concerning
smooth approximation

Author: Christopher J. Bishop
Journal: Proc. Amer. Math. Soc. 124 (1996), 3131-3134
MSC (1991): Primary 46E35
MathSciNet review: 1328340
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Abstract: We answer a question of Smith, Stanoyevitch and Stegenga in the negative by constructing a simply connected planar domain $\Omega $ with no two-sided boundary points and for which every point on $\Omega ^c$ is an $m_2$-limit point of $\Omega ^c$ and such that $C^\infty (\overline {\Omega })$ is not dense in the Sobolev space $W^{k,p}(\Omega )$.

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Additional Information

Christopher J. Bishop
Affiliation: Department of Mathematics, SUNY at Stony Brook, Stony Brook, New York 11794-3651

Keywords: Sobolev spaces, smooth approximation
Received by editor(s): November 23, 1994
Received by editor(s) in revised form: April 3, 1995
Additional Notes: The author is partially supported by NSF Grant DMS 92-04092 and an Alfred P. Sloan research fellowship
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1996 American Mathematical Society