Lower semicontinuity via W^1,q-quasiconvexity

2011/06/14 by Mandallena, Jean-Philippe
#Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1106.2828

Abstract

We isolate a general condition, that we call "localization principle", on the integrand L:\MM→[0,∞], assumed to be continuous, under which W^1,q-quasiconvexity with q∈[1,∞] is a sufficient condition for I(u)=∫_ΩL(∇ u(x))dx to be sequentially weakly lower semicontinuous on W^1,p(Ω;\RR^m) with p∈]1,∞[. Some applications are given.

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