Compensated compactness for higher order differential relations
Andrija Raguž · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 2001
Abstract In this paper we present two compensated compactness results which generalise well known results of Tartar and Murat. The first result generalises the basic compensated compactness theorem in quadratic case to differential relations of arbitrary order m. A particular result of this type has already been used in the homogenisation theory for elastic materials (Antonic and Balenovic, 1999). The other result treats the case where differential relations are of different order, and therefore cannot be reduced to the above form. Nevertheless, we obtain a result showing that we can pass to the limit in the product of two weakly converging sequences.