Issue |
ESAIM: COCV
Volume 12, Number 3, July 2006
|
|
---|---|---|
Page(s) | 371 - 397 | |
DOI | https://doi.org/10.1051/cocv:2006012 | |
Published online | 20 June 2006 |
Towards a two-scale calculus
Università degli Studi di Trento,
Dipartimento di Matematica,
via Sommarive 14,
38050 Povo (Trento), Italia; Visintin@science.unitn.it
Received:
9
September
2004
Revised:
5
April
2005
We define and characterize weak and strong two-scale convergence in Lp, C0 and other spaces via a transformation of variable, extending Nguetseng's definition. We derive several properties, including weak and strong two-scale compactness; in particular we prove two-scale versions of theorems of Ascoli-Arzelà, Chacon, Riesz, and Vitali. We then approximate two-scale derivatives, and define two-scale convergence in spaces of either weakly or strongly differentiable functions. We also derive two-scale versions of the classic theorems of Rellich, Sobolev, and Morrey.
Mathematics Subject Classification: 35B27 / 35J20 / 74Q / 78M40
Key words: Two-scale convergence / two-scale decomposition / Sobolev spaces / homogenization.
© EDP Sciences, SMAI, 2006
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.