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Compensated compactness for higher order differential relations
Author(s) -
Raguz Andrija
Publication year - 2001
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.20010811581
Subject(s) - compact space , mathematics , order (exchange) , limit (mathematics) , type (biology) , differential (mechanical device) , quadratic equation , product (mathematics) , pure mathematics , mathematical analysis , physics , ecology , geometry , finance , economics , biology , thermodynamics
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.