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Manuscripta Mathematica

, Volume 136, Issue 1–2, pp 143–154 | Cite as

Lower semicontinuity for higher order integrals below the growth exponent

  • Flavia GiannettiEmail author
Article
  • 60 Downloads

Abstract

We study the lower semicontinuity of functionals of the form
$$ \mathcal{F}(u)=\int\limits_{\Omega}f(x, u(x), \mathcal{L}u(x))\,dx $$
with respect to the weak convergence in W k,p (Ω), where \({{\mathcal L}}\) is a linear differential operator of order k ≥ 1 and f is quasiconvex with respect to the operator \({{\mathcal L}}\) and satisfies 0 ≤ f(x, s, ξ) ≤ c (1 + |ξ| q ) with qp > 1.

Mathematics Subject Classification (2000)

49N60 49N99 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Dipartimento di Matematica e Applicazioni “R. Caccioppoli”Università di Napoli “Federico II”NapoliItaly

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