On two-scale convergence and related sequential compactness topics
Anders Holmbom, Jeanette Silfver, Nils Svanstedt, Niklas Wellander · Applications of Mathematics · 2006
A general concept of two-scale convergence is introduced and two-scale compactness theorems are stated and proved for some classes of sequences of bounded functions in L 2 (Ω) involving no periodicity assumptions. Further, the relation to the classical notion of compensated compactness and the recent concepts of two-scale compensated compactness and unfolding is discussed and a defect measure for two-scale convergence is introduced.