Several versions of the compensated compactness principle
Svetlana Evgenievna Pastukhova, Anna S Khripunova · Sbornik Mathematics · 2011
The convergence of the product of a solenoidal vector and a gradient in (where is a region in ) is investigated in the case when the factors converge weakly in the spaces and , respectively, with , which means that the main assumption of the classical - lemma fails. Nevertheless, the same convergence (in the sense of distributions in ) as in the framework of the - lemma, survives under certain additional assumptions. The new versions of the compensated compactness principle proved in the paper can be used in homogenization and in the theory of -convergence of monotone operators with non-standard coercivity and growth properties, for instance, some degenerate operators. Bibliography: 20 titles.