Lower semicontinuity via W^{1,q}-quasiconvexity
Classical Analysis and ODEs
2012-12-27 v7 Analysis of PDEs
Abstract
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[. Some applications are given.
Keywords
Cite
@article{arxiv.1106.2828,
title = {Lower semicontinuity via W^{1,q}-quasiconvexity},
author = {Jean-Philippe Mandallena},
journal= {arXiv preprint arXiv:1106.2828},
year = {2012}
}
Comments
13 pages. arXiv admin note: text overlap with arXiv:1107.0072