Power-law approximation under differential constraints

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

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