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...