Sub-criticality of Schroedinger Systems with Antisymmetric Potentials

Abstract

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