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 Publish in OALib Journal ISSN: 2333-9721 APC: Only $99  Views Downloads  Relative Articles$\mathcal{A}\$-quasiconvexity and weak lower semicontinuity of integral functionals On the lower semicontinuity of the ADM mass Lower semicontinuity for an integral functional in BV Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope Weak lower semicontinuity of variational functionals with variable growth A New Extension of Serrin's Lower Semicontinuity Theorem A necessary condition for lower semicontinuity of line energies Quasiconvexity versus group invariance Some Variational Results Using Generalizations of Sequential Lower Semicontinuity Some Variational Results Using Generalizations of Sequential Lower Semicontinuity More...
Mathematics  2011

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

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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.

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