Sub-criticality of Schroedinger Systems with Antisymmetric Potentials

Tristan Rivière

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arXiv · 0911.0988

Sub-criticality of Schroedinger Systems with Antisymmetric Potentials

Tristan Rivière

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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 $Ω$ of the form $$ -Δv=Ωv $$ 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 $q<m/2$.

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Tristan Rivière. 2009-11-05. Sub-criticality of Schroedinger Systems with Antisymmetric Potentials. https://arxiv.org/abs/0911.0988

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