Keywords
- Approximation Property
- Hausdorff Distance
- Extension Property
- Jordan Domain
- Sobolev Function
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
G. Birkhoff and G. Rota, Ordinary differential equations, Ginn & Company, 1962.
A.P. Calderon, Proc. Symp. Pure Math., 4 (1961), 33–41.
H. Federer, Geometric measure theory, Springer-Verlag, 1969.
L.E. Fraenkel, On regularity of the boundary in the theory of Sobolev spaces, Proc. London Math. Soc., (3) (1979), 385–427.
V.M. Gol'dshtein, Extension of functions with generalized first derivatives, English translation: Soviet Mathematics Doklady, 23 (1981), 255–257.
L.I. Hedberg, Non-linear potentials and approximation in the mean by analytic functions, Math. Z., 129 (1972), 299–319.
L.I. Hedberg and T. Wolff, Thin sets in nonlinear potential theory, Ann. Inst. Fourier, 33–4 (1983), 161–187.
P. Jones, Quasiconformal mappings and extendability of functions in Sobolev spaces, Acta Math., 147 (1982), 71–88.
T. Kolsrud, Approximation by smooth functions in Sobolev spaces, a counterexample, Bull. Lond. Math. Soc., 13 (1981), 167–169.
J.L. Lewis, Approximation of Sobolev functions in Jordan domains, to appear in Arkiv för Mat.
V.G. Mazýa, Extension of functions from Sobolev spaces, English translation: Journal of Soviet Mathematics, 22 (1983), 1851–1855.
N. Meyers and J. Serrin, H=W, Proc. Nat. Acad. Sci. U.S.A., 51 (1964), 1055–1056.
E. Stein, Singular integrals and differentiability properties of functions, Princeton University Press, 1970.
S.K. Vodop'yanov, V.M. Gol'dshtein, and T.G. Latfullin, Criteria for extension of functions of the class L 12 from unbounded plane domains, English translation: Siberian Mathematical Journal, 20 (1979), 298–300.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Additional information
To my teacher and advisor, Maurice Heins, on his 70th birthday.
Rights and permissions
Copyright information
© 1987 Springer-Verlag
About this paper
Cite this paper
Lewis, J.L. (1987). Approximations of sobolev functions and related topics. In: Berenstein, C.A. (eds) Complex Analysis I. Lecture Notes in Mathematics, vol 1275. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078355
Download citation
DOI: https://doi.org/10.1007/BFb0078355
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-18356-3
Online ISBN: 978-3-540-47899-7
eBook Packages: Springer Book Archive
