English

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

Analysis of PDEs 2015-08-27 v1

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, Euler-Lagrange equations of conformally invariant variational functionals as Rivi\`ere treated them, and also Euler-Lagrange equations of fractional harmonic maps introduced by Da Lio-Rivi\`ere. In particular, the arguments presented here give new and uniform proofs of the regularity results by Rivi\`ere, Rivi\`ere-Struwe, Da-Lio-Rivi\`ere, and also the integrability results by Sharp-Topping and Sharp, not discriminating between the classical local, and the non-local situations.

Keywords

Cite

@article{arxiv.1205.2852,
  title  = {\epsilon-regularity for systems involving non-local, antisymmetric operators},
  author = {Armin Schikorra},
  journal= {arXiv preprint arXiv:1205.2852},
  year   = {2015}
}
R2 v1 2026-06-21T21:03:02.152Z