Lower semicontinuity via W^{1,q}-quasiconvexity

Details Lower semicontinuity via W^{1,q}-quasiconvexity Lower semicontinuity via W^{1,q}-quasiconvexity

2011-06-14

arxiv.org/abs/1106.2828v2

Mathematics

Classical Analysis and ODEs

10 pages

Scientific paper

We isolate a general condition, that we call "localization principle", on the integrand L:\MM\to[0,\infty], assumed to be continuous, under which W^{1,q}-quasiconvexity with q\in[1,\infty] is a sufficient condition for I(u)=\int_\Omega L(\nabla u(x))dx to be sequentially weakly lower semicontinuous on W^{1,p}(\Omega;\RR^m) with p\in]1,\infty[. We show that this "localization principle" is satisfied under hypotheses on L which are related to the concept of fast growth integrand introduced by Sychev.

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