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Lower semicontinuity for higher order integrals below the growth exponent

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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 q ≥ p > 1.

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  1. Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli “Federico II”, Via Cintia, 80126, Napoli, Italy

    Flavia Giannetti

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  1. Flavia Giannetti
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Giannetti, F. Lower semicontinuity for higher order integrals below the growth exponent. manuscripta math. 136, 143–154 (2011). https://doi.org/10.1007/s00229-011-0434-0

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