-quasiconvexity: weak-star convergence and the gap
Irene Fonseca, Stefan Müller, and Giovanni Leoni
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Submission date: 11. Feb. 2003
published in: Annales de l'Institut Henri Poincaré / C, 21 (2004) 2, p. 209-236
DOI number (of the published article): 10.1016/j.anihpc.2003.01.003
MSC-Numbers: 35E99, 49J45, 74B20
Keywords and phrases: a-quasiconvexity, gap, non-standard growth conditions, lower semicontinuity, sobolev embedding theorem, radon-nikodym decomposition theorem
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Lower semicontinuity results with respect to weak- convergence in the sense of measures and with respect to weak convergence in are obtained for functionals
where admissible sequences satisfy a first order system of PDEs . We suppose that has constant rank, f is -quasiconvex and satisfies the non standard growth conditions
with for , for p>N-1. In particular, our results generalize earlier work where reduced to for some .