A global regularity theory for shpere-valued fractional harmonic maps
Analysis of PDEs
2024-09-05 v1
Abstract
In this paper we consider sphere-valued stationary/minimizing fractional harmonic mappings introduced in recent years by several authors, especially by Millot-Pegon-Schikorra \cite{Millot-Pegon-Schikorra-2021-ARMA} and Millot-Sire \cite{Millot-Sire-15}. Based on their rich partial regularity theory, we establish a quantitative stratification theory for singular sets of these mappings by making use of the quantitative differentiation approach of Cheeger-Naber \cite{Cheeger-Naber-2013-CPAM}, from which a global regularity estimates follows.
Keywords
Cite
@article{arxiv.2409.02442,
title = {A global regularity theory for shpere-valued fractional harmonic maps},
author = {Yu He and ChangLin Xiang and GaoFeng Zheng},
journal= {arXiv preprint arXiv:2409.02442},
year = {2024}
}