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ε-regularity for systems involving non-local, antisymmetric operators

We prove an epsilon-regularity theorem for critical and super-critical systems with a non-local antisymmetric operator on the right-hand side. These systems contain as special cases, Euler-Lagrange equations of conformally invariant variational functionals as Rivière treated them, and also Euler-Lagrange equations of fractional harmonic maps introduced by Da Lio-Rivière. In particular, the arguments presented here give new and uniform proofs of the regularity results by Rivière, Rivière-Struwe, Da-Lio-Rivière, and also the integrability results by Sharp-Topping and Sharp, not discriminating between the classical local, and the non-local situations.