Partial regularity for fractional harmonic maps into spheres

Vincent Millot; Marc Pegon; Armin Schikorra

Partial regularity for fractional harmonic maps into spheres

Analysis of PDEs 2020-01-17 v2

Authors: Vincent Millot , Marc Pegon , Armin Schikorra

Abstract

This article addresses the regularity issue for stationary or minimizing fractional harmonic maps into spheres of order $s\in(0,1)$ in arbitrary dimensions. It is shown that such fractional harmonic maps are $C^\infty$ away from a small closed singular set. The Hausdorff dimension of the singular set is also estimated in terms of $s\in(0,1)$ and the stationarity/minimality assumption.

Keywords

harmonic maps regularity theory harmonic functions

Cite

@article{arxiv.1909.11466,
  title  = {Partial regularity for fractional harmonic maps into spheres},
  author = {Vincent Millot and Marc Pegon and Armin Schikorra},
  journal= {arXiv preprint arXiv:1909.11466},
  year   = {2020}
}

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