A global regularity theory for shpere-valued fractional harmonic maps
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910589063790592 |
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| author | He, Yu Xiang, ChangLin Zheng, GaoFeng |
| author_facet | He, Yu Xiang, ChangLin Zheng, GaoFeng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_02442 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A global regularity theory for shpere-valued fractional harmonic maps He, Yu Xiang, ChangLin Zheng, GaoFeng Analysis of PDEs 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. |
| title | A global regularity theory for shpere-valued fractional harmonic maps |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.02442 |