Energies with values in networks and geometric quasiconvexity

We study the asymptotic behaviour, as $\varepsilon\to 0^+$, of the $p$-Dirichlet energy of maps $u\colonΩ\subset\mathbb{R}^2 \to \mathbb{R}^2$ constrained to take values in the rescaled periodic network $\varepsilon\mathcal Z$, where $\mathcal Z$ is a standard square network in $\mathbb{R}^2$. The o