On two-scale convergence and related sequential compactness topics

Anders Holmbom; Jeanette Silfver; Nils Svanstedt; Niklas Wellander

Applications of Mathematics (2006)

  • Volume: 51, Issue: 3, page 247-262
  • ISSN: 0862-7940

Abstract

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A general concept of two-scale convergence is introduced and two-scale compactness theorems are stated and proved for some classes of sequences of bounded functions in L 2 ( Ω ) involving no periodicity assumptions. Further, the relation to the classical notion of compensated compactness and the recent concepts of two-scale compensated compactness and unfolding is discussed and a defect measure for two-scale convergence is introduced.

How to cite

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Holmbom, Anders, et al. "On two-scale convergence and related sequential compactness topics." Applications of Mathematics 51.3 (2006): 247-262. <http://eudml.org/doc/33253>.

@article{Holmbom2006,
abstract = {A general concept of two-scale convergence is introduced and two-scale compactness theorems are stated and proved for some classes of sequences of bounded functions in $L^\{2\}(\Omega )$ involving no periodicity assumptions. Further, the relation to the classical notion of compensated compactness and the recent concepts of two-scale compensated compactness and unfolding is discussed and a defect measure for two-scale convergence is introduced.},
author = {Holmbom, Anders, Silfver, Jeanette, Svanstedt, Nils, Wellander, Niklas},
journal = {Applications of Mathematics},
keywords = {two-scale convergence; compensated compactness; two-scale transform; unfolding; two-scale convergence; compensated compactness; two-scale transform; unfolding},
language = {eng},
number = {3},
pages = {247-262},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On two-scale convergence and related sequential compactness topics},
url = {http://eudml.org/doc/33253},
volume = {51},
year = {2006},
}

TY - JOUR
AU - Holmbom, Anders
AU - Silfver, Jeanette
AU - Svanstedt, Nils
AU - Wellander, Niklas
TI - On two-scale convergence and related sequential compactness topics
JO - Applications of Mathematics
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 3
SP - 247
EP - 262
AB - A general concept of two-scale convergence is introduced and two-scale compactness theorems are stated and proved for some classes of sequences of bounded functions in $L^{2}(\Omega )$ involving no periodicity assumptions. Further, the relation to the classical notion of compensated compactness and the recent concepts of two-scale compensated compactness and unfolding is discussed and a defect measure for two-scale convergence is introduced.
LA - eng
KW - two-scale convergence; compensated compactness; two-scale transform; unfolding; two-scale convergence; compensated compactness; two-scale transform; unfolding
UR - http://eudml.org/doc/33253
ER -

References

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  12. Two-scale convergence, Int. J.  Pure Appl. Math. 2 (2002), 35–86. (2002) MR1912819
  13. 10.1081/NFA-100103791, Numer. Funct. Anal. Optimization 22 (2001), 127–158. (2001) MR1841866DOI10.1081/NFA-100103791
  14. 10.1023/B:APOM.0000027218.04167.9b, Appl. Math. 49 (2004), 97–110. (2004) Zbl1099.35012MR2043076DOI10.1023/B:APOM.0000027218.04167.9b
  15. 10.1137/0520043, SIAM J.  Math. Anal.   20 (1989), 608–623. (1989) Zbl0688.35007MR0990867DOI10.1137/0520043
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