Displaying similar documents to “ Σ -convergence of nonlinear monotone operators in perforated domains with holes of small size”

Some remarks on two-scale convergence and periodic unfolding

Jan Franců, Nils E M Svanstedt (2012)

Applications of Mathematics

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The paper discusses some aspects of the adjoint definition of two-scale convergence based on periodic unfolding. As is known this approach removes problems concerning choice of the appropriate space for admissible test functions. The paper proposes a modified unfolding which conserves integral of the unfolded function and hence simplifies the proofs and its application in homogenization theory. The article provides also a self-contained introduction to two-scale convergence and gives...

Towards a two-scale calculus

Augusto Visintin (2006)

ESAIM: Control, Optimisation and Calculus of Variations

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We define and characterize weak and strong in , and other spaces 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...