The density of infinitely differentiable functions in Sobolev spaces with mixed boundary conditions

Pavel Doktor; Alexander Ženíšek

Applications of Mathematics (2006)

  • Volume: 51, Issue: 5, page 517-547
  • ISSN: 0862-7940

Abstract

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We present a detailed proof of the density of the set C ∞ ( Ω ¯ ) ∩ V in the space of test functions V ⊂ H 1 ( Ω ) that vanish on some part of the boundary ∂ Ω of a bounded domain Ω .

How to cite

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Doktor, Pavel, and Ženíšek, Alexander. "The density of infinitely differentiable functions in Sobolev spaces with mixed boundary conditions." Applications of Mathematics 51.5 (2006): 517-547. <http://eudml.org/doc/33265>.

@article{Doktor2006,
abstract = {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 $.},
author = {Doktor, Pavel, Ženíšek, Alexander},
journal = {Applications of Mathematics},
keywords = {density theorems; finite element method; density theorems; finite element method},
language = {eng},
number = {5},
pages = {517-547},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The density of infinitely differentiable functions in Sobolev spaces with mixed boundary conditions},
url = {http://eudml.org/doc/33265},
volume = {51},
year = {2006},
}

TY - JOUR
AU - Doktor, Pavel
AU - Ženíšek, Alexander
TI - The density of infinitely differentiable functions in Sobolev spaces with mixed boundary conditions
JO - Applications of Mathematics
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 5
SP - 517
EP - 547
AB - 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 $.
LA - eng
KW - density theorems; finite element method; density theorems; finite element method
UR - http://eudml.org/doc/33265
ER -

References

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  1. Sobolev Spaces, Academic Press, New York-San Francisco-London, 1975. (1975) Zbl0314.46030MR0450957
  2. On some families of functional spaces. Imbedding and continuation theorems, Doklad. Akad. Nauk SSSR 126 (1959), 1163–1165. (Russian) (1959) Zbl0097.09701MR0107165
  3. The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978. (1978) Zbl0383.65058MR0520174
  4. On the density of smooth functions in certain subspaces of Sobolev space, Commentat. Math. Univ. Carol. 14 (1973), 609–622. (1973) Zbl0268.46036MR0336317
  5. Function Spaces, Academia, Praha, 1977. (1977) MR0482102
  6. Boundary properties of functions from “weight” classes, Sov. Math. Dokl. 1 (1960), 589–593. (1960) Zbl0106.30802MR0123103
  7. Les méthodes directes en théorie des équations elliptiques, Academia, Praha, 1967. (1967) MR0227584
  8. A Course in Higher Mathematics  V, Gosudarstvennoje izdatelstvo fiziko-matematičeskoj literatury, Moskva, 1960. (Russian) (1960) 
  9. An imbedding theorem for S. L. Sobolev’s classes  W p r of fractional order, Sov. Math. Dokl. 1 (1960), 132–133. (1960) MR0124731
  10. Sobolev Spaces and Their Applications in the Finite Element Method, VUTIUM, Brno, 2005. (2005) 

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