# Towards a two-scale calculus

ESAIM: Control, Optimisation and Calculus of Variations (2006)

- Volume: 12, Issue: 3, page 371-397
- ISSN: 1292-8119

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topVisintin, Augusto. "Towards a two-scale calculus." ESAIM: Control, Optimisation and Calculus of Variations 12.3 (2006): 371-397. <http://eudml.org/doc/249669>.

@article{Visintin2006,

abstract = {
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.
},

author = {Visintin, Augusto},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Two-scale convergence;
two-scale decomposition;
Sobolev spaces;
homogenization.; two-scale convergence; two-scale decomposition; two-scale convolution},

language = {eng},

month = {6},

number = {3},

pages = {371-397},

publisher = {EDP Sciences},

title = {Towards a two-scale calculus},

url = {http://eudml.org/doc/249669},

volume = {12},

year = {2006},

}

TY - JOUR

AU - Visintin, Augusto

TI - Towards a two-scale calculus

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2006/6//

PB - EDP Sciences

VL - 12

IS - 3

SP - 371

EP - 397

AB -
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.

LA - eng

KW - Two-scale convergence;
two-scale decomposition;
Sobolev spaces;
homogenization.; two-scale convergence; two-scale decomposition; two-scale convolution

UR - http://eudml.org/doc/249669

ER -

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