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Article Dans Une Revue Bulletin des Sciences Mathématiques Année : 2013

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

Résumé

We isolate a general condition, that we call "localization principle", on the integrand $L:\mathbb{M}\to[0,\infty]$, 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 $W^{1,p}(\Omega;\mathbb{R}^m)$ with $p\in]1,\infty[$. Some applications are given.

Dates et versions

hal-01399651 , version 1 (20-11-2016)

Identifiants

Citer

Jean-Philippe Mandallena. Lower semicontinuity via W^{1,q}-quasiconvexity. Bulletin des Sciences Mathématiques, 2013, Bulletin des Sciences Mathématiques, 137 (5), pp.602-616. ⟨10.1016/j.bulsci.2012.12.004⟩. ⟨hal-01399651⟩

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