Sub-criticality of non-local Schrödinger systems with antisymmetric potentials and applications to half-harmonic maps

Abstract: We consider non-local linear Schrödinger-type critical systems of the type where Ω is antisymmetric potential in , v is an valued map and Ωv denotes the matrix multiplication. We show that every solution of (1) is in fact in , for every , in other words, we prove that the system (1) which is a-priori only critical in happens to have a subcritical behavior for antisymmetric potentials. As an application we obtain the regularity of weak 1/2-harmonic maps into compact sub-manifolds without boundary. [Copyright &y& Elsevier]