We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
MiS Preprint
41/2012
$\epsilon$-regularity for systems involving non-local, antisymmetric operators
Armin Schikorra
Abstract
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.
