On compactness results for multi-scale convergence. (English) Zbl 0946.46021

Relative compactness results for two-scale convergence in homogenization were recently extended to the multi-scale case. Here, a much simpler proof is provided by deriving the \(H^1\)-type result from combining the first extension result with the fact that the above-mentioned image space is also the space of all rotation-free fields.


46B50 Compactness in Banach (or normed) spaces
Full Text: DOI


[1] Alt, Lineare Funktionalanalysis (1992)
[2] Allaire, Proc. R. Soc. Edinb. A 126 pp 297– (1996) · Zbl 0866.35017
[3] DOI: 10.1137/0523084 · Zbl 0770.35005
[4] DOI: 10.1007/BFb0084935
[5] DOI: 10.1214/aop/1176996665 · Zbl 0285.60002
[6] DOI: 10.1137/0520043 · Zbl 0688.35007
[7] DOI: 10.1137/0322035 · Zbl 0549.49005
[8] Neveu, Bases mathématiques du calcul des probabilités (1964)
[9] Dellacherie, Probabilités et potentiel (1975)
[10] Dautray, Mathematical analysis and numerical methods for science and technology 3 (1990) · Zbl 0784.73001
[11] Balder, Cahiers du Centre de Recherche de Mathématiques de la Décision 9517 (1995)
[12] DOI: 10.1016/0022-247X(88)90096-0 · Zbl 0664.28003
[13] DOI: 10.1002/cpa.3160450304 · Zbl 0794.35014
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.