| Title:
|
Extensions from the Sobolev spaces $H^1$ satisfying prescribed Dirichlet boundary conditions (English) |
| Author:
|
Ženíšek, Alexander |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
49 |
| Issue:
|
5 |
| Year:
|
2004 |
| Pages:
|
405-413 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Extensions from $H^1(\Omega _P)$ into $H^1(\Omega )$ (where $\Omega _P\subset \Omega $) are constructed in such a way that extended functions satisfy prescribed boundary conditions on the boundary $\partial \Omega $ of $\Omega $. The corresponding extension operator is linear and bounded. (English) |
| Keyword:
|
extensions satisfying prescribed boundary conditions |
| Keyword:
|
Nikolskij extension theorem |
| MSC:
|
46E35 |
| MSC:
|
46N40 |
| MSC:
|
65N99 |
| idZBL:
|
Zbl 1099.65126 |
| idMR:
|
MR2086086 |
| DOI:
|
10.1023/B:APOM.0000048120.75291.a5 |
| . |
| Date available:
|
2009-09-22T18:19:02Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134576 |
| . |
| Reference:
|
[1] A. Kufner, O. John, and S. Fučík: Function Spaces.Academia, Prague, 1977. MR 0482102 |
| Reference:
|
[2] J. Nečas: Les Méthodes Directes en Théorie des Equations Elliptiques.Academia/Masson, Prague/Paris, 1967. MR 0227584 |
| Reference:
|
[3] J. Nečas, I. Hlaváček: Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction.Elsevier, Amsterdam, 1981. MR 0600655 |
| Reference:
|
[4] A. Ženíšek: Finite element variational crimes in parabolic-elliptic problems. Part I. Nonlinear schemes.Numer. Math. 55 (1989), 343–376. MR 0993476, 10.1007/BF01390058 |
| Reference:
|
[5] A. Ženíšek: Nonlinear Elliptic and Evolution Problems and their Finite Element Approximations.Academic Press, London, 1990. MR 1086876 |
| Reference:
|
[6] A. Ženíšek: On a generalization of Nikolskij’s extension theorem in the case of two variables.Appl. Math. 48 (2003), 367–404. Zbl 1099.46022, MR 2008890, 10.1023/B:APOM.0000024482.61562.2b |
| Reference:
|
[7] M. Zlámal: Finite element solution of quasistationary nonlinear magnetic field.RAIRO Anal. Numér. 16 (1982), 161–191. MR 0661454, 10.1051/m2an/1982160201611 |
| Reference:
|
[8] M. Zlámal: A linear scheme for the numerical solution of nonlinear quasistationary magnetic fields.Math. Comput. 41 (1983), 425–440. MR 0717694, 10.1090/S0025-5718-1983-0717694-1 |
| . |
