Lack of Compactness in Two-Scale Convergence
Marc Briane, Juan Casado‐Díaz · SIAM Journal on Mathematical Analysis · 2005
This article deals with the links between compensated compactness and two-scale convergence. More precisely, we ask the following question: Is the div-curl compactness assumption sufficient to pass to the limit in a product of two sequences which two-scale converge with respect to the pair of variables $(x,{x/\varepsilon})$? We reply in the negative. Indeed, the div-curl assumption allows us to control oscillations which are faster than ${1/\varepsilon}$ but not the slower ones.