| Title:
|
The density of infinitely differentiable functions in Sobolev spaces with mixed boundary conditions (English) |
| Author:
|
Doktor, Pavel |
| Author:
|
Ženíšek, Alexander |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
51 |
| Issue:
|
5 |
| Year:
|
2006 |
| Pages:
|
517-547 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We present a detailed proof of the density of the set $C^\infty (\overline{\Omega })\cap V$ in the space of test functions $V\subset H^1(\Omega )$ that vanish on some part of the boundary $\partial \Omega $ of a bounded domain $\Omega $. (English) |
| Keyword:
|
density theorems |
| Keyword:
|
finite element method |
| MSC:
|
46E35 |
| MSC:
|
46N40 |
| idZBL:
|
Zbl 1164.46322 |
| idMR:
|
MR2261637 |
| DOI:
|
10.1007/s10492-006-0019-5 |
| . |
| Date available:
|
2009-09-22T18:27:10Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134651 |
| . |
| Reference:
|
[1] R. A. Adams: Sobolev Spaces.Academic Press, New York-San Francisco-London, 1975. Zbl 0314.46030, MR 0450957 |
| Reference:
|
[2] O. V. Besov: On some families of functional spaces. Imbedding and continuation theorems.Doklad. Akad. Nauk SSSR 126 (1959), 1163–1165. (Russian) Zbl 0097.09701, MR 0107165 |
| Reference:
|
[3] P. G. Ciarlet: The Finite Element Method for Elliptic Problems.North-Holland, Amsterdam, 1978. Zbl 0383.65058, MR 0520174 |
| Reference:
|
[4] P. Doktor: On the density of smooth functions in certain subspaces of Sobolev space.Commentat. Math. Univ. Carol. 14 (1973), 609–622. Zbl 0268.46036, MR 0336317 |
| Reference:
|
[5] A. Kufner, O. John, and S. Fučík: Function Spaces.Academia, Praha, 1977. MR 0482102 |
| Reference:
|
[6] P. I. Lizorkin: Boundary properties of functions from “weight” classes.Sov. Math. Dokl. 1 (1960), 589–593. Zbl 0106.30802, MR 0123103 |
| Reference:
|
[7] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Praha, 1967. MR 0227584 |
| Reference:
|
[8] V. I. Smirnov: A Course in Higher Mathematics V.Gosudarstvennoje izdatelstvo fiziko-matematičeskoj literatury, Moskva, 1960. (Russian) |
| Reference:
|
[9] S. V. Uspenskij: An imbedding theorem for S. L. Sobolev’s classes $W_p^r$ of fractional order.Sov. Math. Dokl. 1 (1960), 132–133. MR 0124731 |
| Reference:
|
[10] A. Ženíšek: Sobolev Spaces and Their Applications in the Finite Element Method.VUTIUM, Brno, 2005. |
| . |
