On a generalization of Nikolskij's extension theorem in the case of two variables

Alexander Ženíšek

Applications of Mathematics (2003)

  • Volume: 48, Issue: 5, page 367-404
  • ISSN: 0862-7940

Abstract

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A modification of the Nikolskij extension theorem for functions from Sobolev spaces H k ( Ω ) is presented. This modification requires the boundary Ω to be only Lipschitz continuous for an arbitrary k ; however, it is restricted to the case of two-dimensional bounded domains.

How to cite

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Ženíšek, Alexander. "On a generalization of Nikolskij's extension theorem in the case of two variables." Applications of Mathematics 48.5 (2003): 367-404. <http://eudml.org/doc/33153>.

@article{Ženíšek2003,
abstract = {A modification of the Nikolskij extension theorem for functions from Sobolev spaces $H^k(\Omega )$ is presented. This modification requires the boundary $\partial \Omega $ to be only Lipschitz continuous for an arbitrary $k\in \mathbb \{N\}$; however, it is restricted to the case of two-dimensional bounded domains.},
author = {Ženíšek, Alexander},
journal = {Applications of Mathematics},
keywords = {Whitney’s extension; Calderon’s extension; Nikolskij’s extension; modified Nikolskij’s extension in case of 2D-domains with a Lipschitz continuous boundary; Whitney's extension; Calderon's extension; Nikolskij's extension; modified Nikolskij's extension in case of 2D-domains with a Lipschitz continuous boundary},
language = {eng},
number = {5},
pages = {367-404},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On a generalization of Nikolskij's extension theorem in the case of two variables},
url = {http://eudml.org/doc/33153},
volume = {48},
year = {2003},
}

TY - JOUR
AU - Ženíšek, Alexander
TI - On a generalization of Nikolskij's extension theorem in the case of two variables
JO - Applications of Mathematics
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 48
IS - 5
SP - 367
EP - 404
AB - A modification of the Nikolskij extension theorem for functions from Sobolev spaces $H^k(\Omega )$ is presented. This modification requires the boundary $\partial \Omega $ to be only Lipschitz continuous for an arbitrary $k\in \mathbb {N}$; however, it is restricted to the case of two-dimensional bounded domains.
LA - eng
KW - Whitney’s extension; Calderon’s extension; Nikolskij’s extension; modified Nikolskij’s extension in case of 2D-domains with a Lipschitz continuous boundary; Whitney's extension; Calderon's extension; Nikolskij's extension; modified Nikolskij's extension in case of 2D-domains with a Lipschitz continuous boundary
UR - http://eudml.org/doc/33153
ER -

References

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  2. The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978. (1978) Zbl0383.65058MR0520174
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  5. Function Spaces, Academia, Prague, 1977. (1977) MR0482102
  6. Les méthodes directes en théorie des équations elliptiques, Academia, Prague/Masson, Paris, 1967. (1967) MR0227584
  7. On imbedding theorems, extensions and approximations of differentiable functions in many variables, Uspekhi Mat. Nauk 16 (1961), 63–111. (Russian) (1961) MR0149267
  8. Variational Difference Methods for the Solution of Elliptic Problems, Izdat. Akad. Nauk ArSSR, Jerevan, 1979. (Russian) (1979) 
  9. 10.1090/S0002-9947-1934-1501735-3, Trans. Amer. Math. Soc. 36 (1936), 63–89. (1936) MR1501735DOI10.1090/S0002-9947-1934-1501735-3
  10. Nonlinear Elliptic and Evolution Problems and their Finite Element Approximations, Academic Press, London, 1990. (1990) MR1086876
  11. Finite element variational crimes in the case of semiregular elements, Appl. Math. 41 (1996), 367–398. (1996) MR1404547

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