Smooth approximation in weighted Sobolev spaces

Tero Kilpeläinen

Commentationes Mathematicae Universitatis Carolinae (1997)

  • Volume: 38, Issue: 1, page 29-35
  • ISSN: 0010-2628

Abstract

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We give necessary and sufficient conditions for the equality H = W in weighted Sobolev spaces. We also establish a Rellich-Kondrachov compactness theorem as well as a Lusin type approximation by Lipschitz functions in weighted Sobolev spaces.

How to cite

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Kilpeläinen, Tero. "Smooth approximation in weighted Sobolev spaces." Commentationes Mathematicae Universitatis Carolinae 38.1 (1997): 29-35. <http://eudml.org/doc/248050>.

@article{Kilpeläinen1997,
abstract = {We give necessary and sufficient conditions for the equality $H=W$ in weighted Sobolev spaces. We also establish a Rellich-Kondrachov compactness theorem as well as a Lusin type approximation by Lipschitz functions in weighted Sobolev spaces.},
author = {Kilpeläinen, Tero},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {weighted Sobolev spaces; Poincaré inequality; Sobolev space; Poincaré inequality; doubling weight; compact imbedding},
language = {eng},
number = {1},
pages = {29-35},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Smooth approximation in weighted Sobolev spaces},
url = {http://eudml.org/doc/248050},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Kilpeläinen, Tero
TI - Smooth approximation in weighted Sobolev spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 1
SP - 29
EP - 35
AB - We give necessary and sufficient conditions for the equality $H=W$ in weighted Sobolev spaces. We also establish a Rellich-Kondrachov compactness theorem as well as a Lusin type approximation by Lipschitz functions in weighted Sobolev spaces.
LA - eng
KW - weighted Sobolev spaces; Poincaré inequality; Sobolev space; Poincaré inequality; doubling weight; compact imbedding
UR - http://eudml.org/doc/248050
ER -

References

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  10. Kufner A., Weighted Sobolev Spaces, Wiley New York (1985). (1985) Zbl0579.35021MR0802206
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  12. Liu F.-C., A Lusin type property of Sobolev functions, Indiana Univ. Math. J. 26 (1977), 645-651. (1977) MR0450488
  13. Meyers N., Serrin J., H = W , Proc. Nat. Acad, Sci. USA 51 (1964), 1055-1056. (1964) Zbl0123.30501MR0164252
  14. Stein E.M., Harmonic Analysis, Princeton University Press Princeton, New Jersey (1993). (1993) Zbl0821.42001MR1232192
  15. Turesson B.O., Nonlinear potential theory and weighted Sobolev spaces, Thesis, University of Linköping, 1995. Zbl0949.31006MR1371571

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