A counterexample concerning smooth approximation
HTML articles powered by AMS MathViewer
- by Christopher J. Bishop PDF
- Proc. Amer. Math. Soc. 124 (1996), 3131-3134 Request permission
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 $W^{k,p}(\Omega )$.References
- Norman G. Meyers and James Serrin, $H=W$, Proc. Nat. Acad. Sci. U.S.A. 51 (1964), 1055–1056. MR 164252, DOI 10.1073/pnas.51.6.1055
- Wayne Smith, Alexander Stanoyevitch, and David A. Stegenga, Smooth approximation of Sobolev functions on planar domains, J. London Math. Soc. (2) 49 (1994), no. 2, 309–330. MR 1260115, DOI 10.1112/jlms/49.2.309
Additional Information
- Christopher J. Bishop
- Affiliation: Department of Mathematics, SUNY at Stony Brook, Stony Brook, New York 11794-3651
- MR Author ID: 37290
- Email: bishop@math.sunysb.edu
- 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
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 3131-3134
- MSC (1991): Primary 46E35
- DOI: https://doi.org/10.1090/S0002-9939-96-03383-7
- MathSciNet review: 1328340