Published Paper
Inserted: 16 dec 2013
Last Updated: 26 dec 2017
Journal: SIAM J MATH ANAL
Volume: 46
Number: 2
Pages: 1085-1115
Year: 2014
Abstract:
We study the $\Gamma$-convergence of the power-law functionals \[ F_p(V)=\Bigl(\int_{\Omega} f^p(x, V(x))dx\Bigr)^{1/ p}, \] as $p$ tends to $+\infty$, in the setting of constant-rank operator $\cal A$. We show that the $\Gamma$-limit is given by a supremal functional on $L^{\infty}(\Omega;\mathbb{M}^{d\times N}) \cap \hbox {Ker} \cal A$ where $\mathbb{M}^{d\times N}$ is the space of $d\times N$ real matrices. We give an explicit representation formula for the supremand function. We provide some examples and as application of the $\Gamma$-convergence results we characterize the strength set in the context of electrical resistivity.
Keywords: Supremal functionals, $\Gamma$-convergence, $L^p$-approximation, Lower semicontinuity, $\cal A$-quasiconvexity.
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