A-quasiconvexity, lower semicontinuity and Young measures
Stefan Müller and Irene Fonseca
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Submission date: 06. Jun. 1998
published in: SIAM journal on mathematical analysis, 30 (1999) 6, p. 1355-1390 (electronic)
DOI number (of the published article): 10.1137/S0036141098339885
MSC-Numbers: 35D99, 35E99, 49J45
Keywords and phrases: a-quasiconvexity, equi-integrability, young measure, lower semicontinuity
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The notion of -quasiconvexity is introduced as a necessary and sufficient condition for (sequential) lower semicontinuity of
whenever is a normal integrand, is open, bounded, in measure, in ( if ), and in ( if ). Here is a constant-rank partial differential operator, , and is -quasiconvex if
for all and all such that, , and w is Q-periodic, . The characterization of Young measures generated by such sequences is obtained for , thus recovering the well known results for the framework curl, i.e. when for some , . In this case -quasiconvexity reduces to Morrey's notion of quasiconvexity.