The three divergence free matrix fields problem

Mariapia Palombaro, Marcello Ponsiglione

We prove that for any connected open set $\Omega \subset {\mathbb{R}}^n$ and for any set of matrices $K=\{A_1,A_2,A_3\}\subset M^{m\times n}$, with $m\ge n$ and rank$(A_i-A_j)=n$ for $i\ne j$, th…