Sub-criticality of Schroedinger Systems with Antisymmetric Potentials

Details Sub-criticality of Schroedinger Systems with Antisymmetric Potentials Sub-criticality of Schroedinger Systems with Antisymmetric Potentials

2009-11-05

arxiv.org/abs/0911.0988v1

Mathematics

Analysis of PDEs

Scientific paper

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

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