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MiS Preprint

$\epsilon$-regularity for systems involving non-local, antisymmetric operators

Armin Schikorra


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, both, Euler-Lagrange equations of conformally invariant variational functionals as Riviere treated them, and also Euler-Lagrange equations of fractional harmonic maps introduced by Da Lio-Riviere.

In particular, the arguments give new and uniform proofs of the regularity results by Riviere, Riviere-Struwe, Da-Lio-Riviere, and also the integrability results by Sharp-Topping and Sharp, not discriminating between the classical local, and the non-local situations.

One important ingredient for this kind of stability, relies on the proof of uniformity of Hardy-space estimates for bi-commutators as the leading differential order goes to two.

MSC Codes:
58E20, 35B65, 35J60
harmonic maps, nonlinear elliptic pde, regularity of solutions

Related publications

2015 Repository Open Access
Armin Schikorra

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

In: Calculus of variations and partial differential equations, 54 (2015) 4, pp. 3531-3570