Sub-criticality of Schroedinger Systems with Antisymmetric Potentials

Let $m$ be an integer larger or equal to 3. We prove that Schroedinger systems on $B^m$ with $L^{m\mathrm{/}2}-$antisymmetric potential $\mathrm{\Omega }$ of the form $$-\mathrm{\Delta }v=\mathrm{\Omega }v$$ can be written in divergence form and we deduce that solutions $v$ in $L^{m\mathrm{/}(m-2)}$ are in fact $W_{loc}^{2,q}$ for any $q<m\mathrm{/}2$.