| Title:
|
On a generalization of Nikolskij's extension theorem in the case of two variables (English) |
| Author:
|
Ženíšek, Alexander |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
48 |
| Issue:
|
5 |
| Year:
|
2003 |
| Pages:
|
367-404 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Whitney’s extension |
| Keyword:
|
Calderon’s extension |
| Keyword:
|
Nikolskij’s extension |
| Keyword:
|
modified Nikolskij’s extension in case of 2D-domains with a Lipschitz continuous boundary |
| MSC:
|
46E35 |
| MSC:
|
46E39 |
| MSC:
|
46E99 |
| idZBL:
|
Zbl 1099.46022 |
| idMR:
|
MR2008890 |
| DOI:
|
10.1023/B:APOM.0000024482.61562.2b |
| . |
| Date available:
|
2009-09-22T18:14:27Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134536 |
| . |
| Reference:
|
[1] V. M. Babič: On the extension of functions.Uspekhi Mat. Nauk 8 (1953), 111–113. (Russian) MR 0056675 |
| Reference:
|
[2] P. G. Ciarlet: The Finite Element Method for Elliptic Problems.North-Holland, Amsterdam, 1978. Zbl 0383.65058, MR 0520174 |
| Reference:
|
[3] G. M. Fichtengolc: Differential and Integral Calculus I.Gostechizdat, Moscow, 1951. (Russian) |
| Reference:
|
[4] M. R. Hestenes: Extension of the range of a differentiable function.Duke Math. J. 8 (1941), 183–192. Zbl 0024.38602, MR 0003434, 10.1215/S0012-7094-41-00812-8 |
| Reference:
|
[5] A. Kufner, O. John, S. Fučík: Function Spaces.Academia, Prague, 1977. MR 0482102 |
| Reference:
|
[6] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Prague/Masson, Paris, 1967. MR 0227584 |
| Reference:
|
[7] S. M. Nikolskij: On imbedding theorems, extensions and approximations of differentiable functions in many variables.Uspekhi Mat. Nauk 16 (1961), 63–111. (Russian) MR 0149267 |
| Reference:
|
[8] L. A. Oganesjan, L. A. Ruchovec: Variational Difference Methods for the Solution of Elliptic Problems.Izdat. Akad. Nauk ArSSR, Jerevan, 1979. (Russian) |
| Reference:
|
[9] H. Whitney: Analytic extensions of differentiable functions defined in closed sets.Trans. Amer. Math. Soc. 36 (1936), 63–89. MR 1501735, 10.1090/S0002-9947-1934-1501735-3 |
| Reference:
|
[10] A. Ženíšek: Nonlinear Elliptic and Evolution Problems and their Finite Element Approximations.Academic Press, London, 1990. MR 1086876 |
| Reference:
|
[11] A. Ženíšek: Finite element variational crimes in the case of semiregular elements.Appl. Math. 41 (1996), 367–398. MR 1404547 |
| . |
