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 $\A$. We show that the $\Gamma$-limit is given by a supremal functional on $L^{\infty}(\Omega;\MM) \cap \hbox {Ker} \A$ where $\MM$ 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.
Power-law approximation under differential constraints
PRINARI, Francesca Agnese;
2014-01-01
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 $\A$. We show that the $\Gamma$-limit is given by a supremal functional on $L^{\infty}(\Omega;\MM) \cap \hbox {Ker} \A$ where $\MM$ 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.File in questo prodotto:
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