# Power-law approximation under differential constraints

created by prinari on 16 Dec 2013
modified by ansini on 26 Dec 2017

[BibTeX]

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.