\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.
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}
}