Nguetseng's notion of it two-scale convergence and some of its main properties are first shortly reviewed. The (weak) two-scale limit of the gradient of bounded sequences of is then studied: if weakly in , a sequence is constructed such that and weakly two-scale. Analogous constructions are introduced for the weak two-scale limit of derivatives in the spaces , , , . The application to the two-scale limit of some classical equations of electromagnetism and continuum mechanics is outlined. These results are then applied to the homogenization of quasilinear elliptic equations like .
Cite this article
Augusto Visintin, Two-Scale Convergence of First-Order Operators. Z. Anal. Anwend. 26 (2007), no. 2, pp. 133–164DOI 10.4171/ZAA/1315