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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.16442 |
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| _version_ | 1866916802247786496 |
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| author | Vincent, Akshara |
| author_facet | Vincent, Akshara |
| contents | We show that the mappings $u\in \dot{W}^{s,p}(\mathbb{R}^n,\mathcal{N})$ into manifolds $\mathcal{N}$ of a sufficiently simple topology that minimize the energy $$\int_{\mathbb{R}^n}\int_{\mathbb{R}^n}\frac{|u(x)-u(y)|^p}{|x-y|^{n+sp}} \;dx\;dy$$ are locally Hölder continuous in a bounded domain $Ω$ outside a singular set $Σ$ with Hausdorff dimension strictly smaller than $n-sp$. We avoid the use of a monotonicity formula (which is unknown if $p \neq 2$) by using a blow-up argument instead. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_16442 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hölder continuity of Minimizing $W^{s,p}$-Harmonic Maps Vincent, Akshara Analysis of PDEs We show that the mappings $u\in \dot{W}^{s,p}(\mathbb{R}^n,\mathcal{N})$ into manifolds $\mathcal{N}$ of a sufficiently simple topology that minimize the energy $$\int_{\mathbb{R}^n}\int_{\mathbb{R}^n}\frac{|u(x)-u(y)|^p}{|x-y|^{n+sp}} \;dx\;dy$$ are locally Hölder continuous in a bounded domain $Ω$ outside a singular set $Σ$ with Hausdorff dimension strictly smaller than $n-sp$. We avoid the use of a monotonicity formula (which is unknown if $p \neq 2$) by using a blow-up argument instead. |
| title | Hölder continuity of Minimizing $W^{s,p}$-Harmonic Maps |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2506.16442 |