On regularity and rigidity of $2\times 2$ differential inclusions into non-elliptic curves

Xavier Lamy, Andrew Lorent, Guanying Peng

We study differential inclusions $Du\in \Pi$ in an open set $\Omega \subset {\mathbb{R}}^2$, where $\Pi \subset {\mathbb{R}}^{2\times 2}$ is a compact connected $C^2$ curve without rank-one connecti…