Previous |  Up |  Next

Article

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
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: 2015-05-17
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.
.

Files

Files Size Format View
AplMat_51-2006-5_4.pdf 435.3Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo