We consider the vectorial system \[ \begin{ cases} Du \in \mathcal{ O}(2), & \mbox{ a.e. in}\;\Omega, u=0, & \mbox{ on} \;\partial \Omega, \end{ cases} \] where $\Omega$ is a subset of $\R^2$, $u:\Omega\to \R^2$ and $\mathcal{ O}(2)$ is the orthogonal group of $\R^2$. We provide a variational method to select, among the infinitely many solutions, the ones that minimize an appropriate weighted measure of the singular set of the gradient.
Categories: math.OC math.AP